MESKILL, Circuit Judge:

Defendants Joseph Aracri, John Papandon and Anthony Zummo appeal from judgments of conviction entered after a jury trial before Wexler, J., in the United States District Court for the Eastern District of New York. Defendants were convicted of conspiracy to defraud the United States in violation of 18 U.S.C. § 371 and of aiding and assisting in the preparation of fraudulent federal excise tax returns in violation of 26 U.S.C. § 7206(2). Defendants make various claims of error. For the reasons set forth below, we affirm in part and remand for consideration of whether impeachment material that the government should have disclosed pursuant to Giglio v. United States, 405 U.S. 150, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972), would have affected the outcome of the trial.

BACKGROUND

Defendants' convictions stem from their participation in a scheme to avoid the payment of gasoline excise taxes through a system of fictitious invoices falsely representing that taxes had been paid on sales of gasoline. During the indictment period the Internal Revenue Code, 26 U.S.C. § 1 et seq. (IRC), imposed a nine cent per gallon tax on gasoline sold by producers of gasoline. See IRC § 4081(a) (1984). Sales of gasoline to "producers" were exempted from this tax. See id. § 4083. The definition of "producers" relevant to this appeal included wholesale distributors who elected to register with respect to the tax imposed by obtaining an IRS Form 637, Registration for Tax-Free Transactions. See id. § 4082(a), (d)(2). To conform to the evidence at trial we will refer to registered companies as "licensed companies" and to the registration forms as "licenses." Thus, a licensed wholesale distributor did not have to pay federal excise tax on gasoline sold to another licensed wholesale distributor. The first licensed wholesale distributor who sold gasoline to an unlicensed company was required to pay excise taxes on that sale. New York State had a similar licensing and taxation law.

At trial the government introduced evidence from which the jury reasonably could have found the following facts: Defendants and other individuals set up fictitious paper sales of gasoline through various licensed and unlicensed companies — sometimes referred to as "daisy chains" — to make it appear that excise taxes had been paid on gasoline sales when, in fact, no taxes had been paid. As part of the scheme, the defendants used shell companies that held licenses. This design made it difficult for authorities to trace the real owners in interest of licenses. These shell companies were referred to as "burn" companies and the gasoline that fraudulently was treated as tax-paid gasoline was referred to as "burned" gasoline. The shell companies employed by the defendants changed as the scheme progressed because various authorities cancelled the licenses when they realized that gasoline was being "burned" through them, although unsure by whom. To help the reader understand the scheme, we have included as an Appendix six charts used by the government at trial.

Aracri and Papandon owned and operated Pilot Petroleum Associates, Inc. (Pilot), a licensed wholesale distributor of gasoline. Zummo was the president of Pride Oil Corp. (Pride Oil), a retail gasoline company.

In late 1982, Aracri and Papandon met with a group of individuals, including Lawrence Iorizzo and George Kryssing, both of whom testified at trial, to discuss a scheme to avoid paying gasoline excise taxes by setting up a paper trial of purported gasoline sales. Kryssing and Bernard Short ran Petroleum Haulers, Inc. (Petroleum Haulers), an unlicensed company that could not buy tax-free gasoline. The group agreed that Petroleum Haulers would purchase the license of Pilot International, a company controlled by Aracri and Papandon, in order to create fictitious invoices to make it appear that taxes had been paid on the sale of gasoline when, in fact, they had not been paid. They also agreed that Pilot, a separate company of Aracri's and Papandon's, would be the supplier of the gasoline on which taxes would not be paid.

According to the testimony, as a condition of the sale of the license, Aracri and Papandon insisted that the name of the company on the license be changed. According to Kryssing, the license was owned by an individual named Don Kuss who knew nothing about the scheme. Through the name change, Aracri and Papandon hoped to maintain his ignorance. Iorizzo explained that Aracri and Papandon insisted on the name change in an attempt to conceal their connection to the scheme. Iorizzo arranged for a Panama corporation to acquire the stock of the company. For whatever reason, the group changed the name of the company to Northbrook Associates, Inc. (Northbrook). Kryssing and Short received the license after paying Aracri and Papandon $41,000. Iorizzo acquired the assets of the company through a Panamanian company.

The group carried out this first phase of the scheme as follows. Pilot obtained gasoline from General Oil Distributors, Inc. (General) that legitimately was tax-free gasoline because it was sold by a licensed company to a licensed company. Pilot supplied the gasoline to Petroleum Haulers. Without the scheme Pilot would have incurred tax liability at that point because Petroleum Haulers was an unlicensed company. Through the use of the Northbrook license and fictitious invoices the group made it appear that Northbrook incurred the tax liability on the sale before it was purchased by Petroleum Haulers. The invoices represented that gasoline was transferred from Pilot to Northbrook tax-free and then sold tax-paid by Northbrook to Future Positions, a company controlled by Iorizzo, before it was transferred to Petroleum Haulers. Future Positions would prepare the paperwork stating that federal and state excise taxes had been paid on the gasoline. Petroleum Haulers then sold some of the tax-paid gasoline back to Pilot and the rest to Zummo's company, Pride Oil, or other companies. This method of "burning" gasoline through Northbrook made it appear that Northbrook had paid taxes on the transaction. The taxes in fact had not been paid.

In December 1983, Northbrook's license was cancelled by New York because millions of gallons of gasoline were being transferred through the company and no taxes were being paid on the transfers. Unable to use the Northbrook license to further their tax avoidance scheme, Aracri, Papandon, Kryssing, Short and Sheldon Levine agreed to find another license through which to "burn" gasoline. On Kryssing's request, Zummo located a new license for sale — Cabot Petroleum Products, Inc. (Cabot). The license was desirable because it was considered a "clean license," one that had been "up to date on the filings" and had had "[v]ery little activity on it." Aracri, Papandon, Levine and Short gave Zummo approximately $175,000 to purchase the Cabot license. They set up an office for Cabot and had Zummo mail the license to Cabot's new business address. Yassim Akkurt was named president of Cabot and was the sole signator on all corporate documents. The group planned that if and when tax collectors discovered their scheme Akkurt would abscond to his native Turkey. An unlicensed sham company, Vestal Petroleum Company (Vestal), also was created as an offshoot of Cabot to further the scheme.

Cabot and Vestal were used to prepare invoices representing that General or Rappaport Fuel Company (Rappaport Fuel) — both licensed companies — transferred the gasoline tax-free to Cabot, Cabot transferred gasoline tax-paid to unlicensed Vestal, Vestal transferred the gasoline tax-paid to Petroleum Haulers, and Petroleum Haulers transferred the gasoline tax-paid to Pilot or Pride Oil or Snug Harbor, another company. Cabot, which purportedly incurred the tax liability, never paid taxes on the transactions.

Defendants used Cabot to further their scheme during the first few months of 1984. In March 1984, the Cabot license, like that of its predecessor Northbrook, was cancelled. As planned, Akkurt disappeared, as did the records of Cabot and Vestal.

Once again, Aracri, Papandon, Zummo, Levine and Kryssing were left without a licensed company through which to "burn" gasoline. Around April or May 1984 Zummo and Aracri contacted Iorizzo to discuss "burning" gasoline through Rappaport Fuel. Zummo, Aracri and Iorizzo discussed the matter among themselves and with Ronald Weiner.

In May 1984, defendants utilized Conlo Service, Inc. (Conlo), operated by Weiner, to further their scheme. After Iorizzo asked Weiner to do a favor "to accommodate" Aracri, Kryssing and Aracri met with Weiner. They discussed paying Weiner to prepare fictitious invoices representing that Pilot sold gasoline to licensed Conlo and then Conlo transferred the gasoline to an Iorizzo company — either Rappaport Fuel or Houston Trading — and then to Petroleum Haulers tax-paid. The purpose of Rappaport Fuel and Houston Trading in the "daisy chain" was to avoid paying taxes on the sale.

A three count indictment was filed against Aracri, Papandon and Zummo in the Eastern District of New York on April 25, 1990. Count One of the indictment charged that from December 31, 1982 through August 31, 1984 defendants and other individuals knowingly, willfully and unlawfully combined, conspired, confederated and agreed to defraud the United States Treasury Department and the Internal Revenue Service (IRS) by impeding, impairing, obstructing and defeating their lawful governmental functions in the ascertainment, computation, assessment and collection of revenue through federal gasoline excise taxes, and that they concealed this fact. Counts Two and Three charged defendants with willfully aiding, assisting, procuring and causing General and Rappaport Fuel, respectively, to prepare and present to the IRS a fraudulent and false Quarterly Federal Excise Tax Return, Form 720, for the quarter ending March 31, 1984.

After a seven day trial, the jury returned a general verdict of guilty as to each defendant on all three counts.

Before we heard argument in the case on appeal, the government moved to remand to the district court for consideration of whether newly discovered impeachment materials that the government should have disclosed pursuant to Giglio would have affected the outcome of the trial. We denied the motion because defendants had raised numerous arguments on appeal that, if accepted, would warrant reversal of their convictions barring a new trial. See, e.g., Burks v. United States, 437 U.S. 1, 18, 98 S.Ct. 2141, 2150, 57 L.Ed.2d 1 (1978) ("the Double Jeopardy Clause precludes a second trial once the reviewing court has found the evidence legally insufficient"); United States v. Garcia, 938 F.2d 12, 14 (2d Cir. 1991) ("when an appellate reversal is based on insufficient evidence, a retrial is prohibited") (citation omitted), cert. denied, ___ U.S. ___, 112 S.Ct. 868, 116 L.Ed.2d 774 (1992).

DISCUSSION

A. Count One

Defendants offer numerous challenges to Count One of the indictment. Count One enumerates several "schemes" in furtherance of a conspiracy to defraud the government. Arguably, only one of these schemes is within the applicable statute of limitations period. Defendants argue that the government linked several separate time-barred conspiracies to one timely brought conspiracy in a single count in order to circumvent a statute of limitations bar. They advance numerous specific challenges based on this premise. None of these challenges has merit.

1. Statute of Limitations

Defendants claim that the relevant statute of limitations period for the conspiracy charged in Count One is five years instead of the six year limitations period applied by Judge Wexler. We disagree. The applicable statute of limitations period for conspiracies such as the one charged in this indictment is six years. See United States v. Ingredient Technology Corp., 698 F.2d 88, 98-99 (2d Cir.), cert. denied, 462 U.S. 1131, 103 S.Ct. 3111, 77 L.Ed.2d 1366 (1983). IRC section 6531 provides that the limitations period "for offenses involving the defrauding or attempting to defraud the United States or any agency thereof, whether by conspiracy or not," shall be six years. 26 U.S.C. § 6531(1). Likewise, the IRC provides a six year limitations period "for offenses arising under section 371 of Title 18 of the United States Code, where the object of the conspiracy is to attempt in any manner to evade or defeat any tax or the payment thereof." Id. § 6531(8).

The indictment was filed on April 25, 1990. Based on the evidence at trial, the jury could have convicted defendants for their participation in a conspiracy in which they committed an overt act after April 25, 1984. The judge specifically instructed the jury as follows: "The statute of limitations for the conspiracy charged in the indictment is six years. This means that you cannot find any of the defendants guilty unless the government proves beyond a reasonable doubt that the charged conspiracy existed sometime after April 25, 1984."

There was ample evidence that the conspiracy continued into May 1984. There was testimony that around April 1984 Iorizzo met with Zummo to discuss "burning" gasoline through Rappaport Fuel because the Cabot license had been cancelled. Zummo told Aracri about the discussion and Aracri contacted Iorizzo. In May 1984, Iorizzo, Aracri and Weiner arranged to "burn" gasoline through Conlo and Rappaport. That same month invoices represented that gasoline was sold from General to Pilot to Conlo tax-free and then through Rappaport Fuel and Houston Trading to Petroleum Haulers tax-paid before it was ultimately sold to Pride Oil or Pilot tax-paid. The purpose of this chain of sales was to avoid paying excise taxes and in fact no taxes were paid on these sales. Accordingly, we conclude that the district court applied the appropriate limitations period.

2. Duplicity

Defendants next argue that Count One should have been dismissed as duplicitous because it charged multiple separate and distinct conspiracies in a single count. Accordingly, defendants contend that they were denied the right to a unanimous jury verdict on the only "conspiracy" not barred by the statute of limitations.

An indictment is duplicitous if it joins two or more distinct crimes in a single count. United States v. Murray, 618 F.2d 892, 896 (2d Cir. 1980). A duplicitous indictment, which alleges several offenses in the same count, must be distinguished from "the allegation in a single count of the commission of a crime by several means." Id. The latter is not duplicitous. The policy considerations underlying the prohibition against duplicitous indictments are varied. As we previously have stated, these considerations include

avoiding the uncertainty of whether a general verdict of guilty conceals a finding of guilty as to one crime and a finding of not guilty as to another, avoiding the risk that the jurors may not have been unanimous as to any one of the crimes charged, assuring the defendant adequate notice, providing the basis for appropriate sentencing, and protecting against double jeopardy in a subsequent prosecution.

United States v. Margiotta, 646 F.2d 729, 733 (2d Cir. 1981) (citing Murray, 618 F.2d at 896).

A conspiracy indictment presents "unique issues" in the duplicity analysis because "a single agreement may encompass multiple illegal objects." Murray, 618 F.2d at 896. In this Circuit "it is well established that `[t]he allegation in a single count of a conspiracy to commit several crimes is not duplicitous, for "[t]he conspiracy is the crime and that is one, however diverse its objects."'" Id. (citations omitted); see also Braverman v. United States, 317 U.S. 49, 53, 63 S.Ct. 99, 101, 87 L.Ed. 23 (1942) ("Whether the object of a single agreement is to commit one or many crimes, it is in either case that agreement which constitutes the conspiracy which the statute punishes. The one agreement cannot be taken to be several agreements and hence several conspiracies because it envisages the violation of several statutes rather than one.").

We have declined to accept the law of the Fifth Circuit "that any acts capable of being charged as separate offenses must be alleged in separate counts." Margiotta, 646 F.2d at 733 (citing Bins v. United States, 331 F.2d 390, 393 (5th Cir.), cert. denied, 379 U.S. 880, 85 S.Ct. 149, 13 L.Ed.2d 87 (1964)). Instead, under the law of this Circuit, "acts that could be charged as separate counts of an indictment may instead be charged in a single count if those acts could be characterized as part of a single continuing scheme." United States v. Tutino, 883 F.2d 1125, 1141 (2d Cir. 1989) (citation omitted), cert. denied, 493 U.S. 1081, 110 S.Ct. 1139, 107 L.Ed.2d 1044 (1990). With these principles in mind, we conclude that the indictment at issue charged a single conspiracy to defraud the United States and listed various means of furthering that conspiracy.

Count One charged that defendants and other co-conspirators

did knowingly, willfully and unlawfully combine, conspire, confederate, and agree to defraud the United States Treasury Department and the Internal Revenue Service . . . by impeding, impairing, obstructing and defeating the lawful governmental functions of the Treasury Department and the Internal Revenue Service in the ascertainment, computation, assessment and collection of revenue: to wit, federal gasoline excise taxes, and to conceal this fact.

This type of language has become "customary boiler-plate" in indictments to defraud the United States of taxes in violation of 18 U.S.C. § 371. United States v. Helmsley, 941 F.2d 71, 90 (2d Cir. 1991), cert. denied, ___ U.S. ___, 112 S.Ct. 1162, 117 L.Ed.2d 409 (1992). The indictment alleged that defendants and others created a series of fraudulent and sham paper sales of gasoline among various entities — that is, "daisy chain" transfers. In addition, it alleged that defendants and others created, purchased, obtained and utilized "burn companies" — shell companies that held licenses — such as Northbrook, Cabot and Houston Holdings to make it appear that taxes had been paid on gasoline when those taxes had not and would not be paid. The indictment explained that defendants and others

would at various times use different burn companies and other entities, and would alter the positions of the various entities in the daisy chains. When the defendants . . . and other co-conspirators . . . believed that a particular entity's [license] was no longer useable, they would utilize another burn company to avoid paying and conceal the non-payment of taxes.

The charged conspiracy clearly could be characterized as one continuing scheme that involved utilizing different companies, including "burn" companies, in a series of transfers all for the single purpose of concealing the non-payment of taxes and transferring the liability for paying taxes to "burn" companies and others. See, e.g., Margiotta, 646 F.2d at 733 (rejecting duplicity challenge to indictment charging a scheme to defraud and listing numerous mailings because the essence of the crime charged was carrying out a single scheme to defraud); cf. Tutino, 883 F.2d at 1141 (permitting aggregation of two heroin sales in one count of an indictment because defendants "were involved in an ongoing and continuous drug conspiracy, and . . . the two sales were part of a single continuing scheme"). Therefore, because the essence of the crime charged in Count One is a single scheme to defraud the United States, the indictment is not duplicitous.

3. Multiple Conspiracies versus a Single Conspiracy

Having concluded that the indictment charged one conspiracy, the next issue is whether the evidence at trial proved one conspiracy or proved multiple conspiracies. "When convictions have been obtained on the theory that all defendants were members of a single conspiracy although, in fact, the proof disclosed multiple conspiracies, the error of variance has been committed." United States v. Bertolotti, 529 F.2d 149, 154 (2d Cir. 1975) (citations omitted); see also Helmsley, 941 F.2d at 89. If there is a variance between proof and indictment, the next step is to determine whether defendants "were so prejudiced by the variance as to be entitled to a reversal of their convictions." Bertolotti, 529 F.2d at 155 (citations omitted); see also Helmsley, 941 F.2d at 89 ("Variances are subject to the harmless error rule and thus are not grounds for reversal without a showing of prejudice to the defendant.").

Whether the government has proved a single conspiracy or has instead proved "multiple other independent conspiracies is a question of fact for a properly instructed jury." United States v. Alessi, 638 F.2d 466, 472 (2d Cir. 1980) (citations omitted).

In assessing the contention that the evidence was insufficient to support the jury's conclusion that there was a single conspiracy, we must view the evidence as a whole in the light most favorable to the government and uphold the verdict if, viewed in that light, a rational juror could have concluded beyond a reasonable doubt (1) that the scope of the criminal enterprise proven fits the pattern of the single conspiracy alleged in the indictment, and (2) that the defendant participated in the alleged enterprise with a consciousness of its general nature and extent.

United States v. Beech-Nut Nutrition Corp., 871 F.2d 1181, 1192 (2d Cir.) (citations omitted), cert. denied sub nom. Lavery v. United States, 493 U.S. 933, 110 S.Ct. 324, 107 L.Ed.2d 314 (1989). We find no error in the jury instructions and ample evidence to permit the jury to infer that defendants participated in a single conspiracy to defraud the United States of gasoline excise taxes.

a. Jury Instructions

"[A] multiple conspiracy charge is required whenever several conspiracies might be inferred from the evidence offered." United States v. Cambindo Valencia, 609 F.2d 603, 625 (2d Cir. 1979), cert. denied, 446 U.S. 940, 100 S.Ct. 2163, 64 L.Ed.2d 795 (1980). As we observed in United States v. Barlin, 686 F.2d 81, 88 (2d Cir. 1982):

It is by now commonplace that "in order to promote the goal of `keeping distinct conspiracies distinct,' the court should describe explicitly the possibility of several conspiracies and instruct the jury that in order to convict a given defendant, it must `find that he was a member of the conspiracy charged in the indictment and not some other conspiracy.'"

Id. at 88 (citations omitted); see United States v. Blanco, 861 F.2d 773, 782 (2d Cir. 1988), cert. denied, 489 U.S. 1019, 109 S.Ct. 1139, 103 L.Ed.2d 200 (1989).

The charge in this case satisfied these requirements. Judge Wexler explicitly alerted the jury to the possibility of several conspiracies. He stated: "Although the indictment charges a single conspiracy, it is possible that you will determine there were two or more separate conspiracies, whether there's one conspiracy or more conspiracies, or no conspiracies at all is a question of fact for you to determine." The judge then properly instructed the jury that it must acquit a defendant if it found that the defendant "was a member of a separate conspiracy other than the conspiracy charged in the indictment and [did] not find . . . that such defendant was a member of the conspiracy charged in the indictment."

Defendants argue that reversal is warranted because Judge Wexler refused to charge specifically that if the jury found multiple conspiracies it must acquit. "[I]n reviewing claims of error in the trial court's jury charge, we must consider the challenged portions not in isolation but in light of the instructions as a whole." United States v. Maldonado-Rivera, 922 F.2d 934, 960 (2d Cir. 1990) (citations omitted), cert. denied, ___ U.S. ___, 111 S.Ct. 2858, 115 L.Ed.2d 1025, 1026 (1991). The instruction regarding multiple conspiracies charged in its entirety:

Although the indictment charges a single conspiracy, it is possible that you will determine there were two or more separate conspiracies, whether there's one conspiracy or more conspiracies, or no conspiracies at all is a question of fact for you to determine.

If you find that no conspiracy existed, then you must acquit the defendants on the conspiracy charge. However, if you find beyond a reasonable doubt that such a conspiracy existed, you then must determine whether — who were the members of that conspiracy. If you find that a particular defendant was a member of a separate conspiracy other than the conspiracy charged in the indictment and do not find beyond a reasonable doubt that such defendant was a member of the conspiracy charged in the indictment, then you must acquit the defendant.

In other words, to find a defendant guilty of the conspiracy charge, you must find beyond a reasonable doubt that he was a member of the conspiracy charged in the indictment, not some other conspiracy.

This language is notably similar to language we approved in United States v. Tramunti, 513 F.2d 1087, 1107 (2d Cir.), cert. denied, 423 U.S. 832, 96 S.Ct. 54, 55, 46 L.Ed.2d 50 (1975).

As we observed in Tramunti, although it is preferable to instruct the jury that it must acquit if it finds multiple conspiracies when only one conspiracy is charged, the "failure so to charge is not error where the charge examined as a whole stresses that there must be [a] finding of the single conspiracy charged and individual knowing participation by each individual in it." 513 F.2d at 1108 (citations omitted).

Judge Wexler's charge stressed the necessity of finding that each defendant participated in the single conspiracy charged in the indictment. Although a more detailed charge on the distinction between multiple conspiracies and a single conspiracy may have been desirable, see, e.g., Beech-Nut Nutrition Corp., 871 F.2d at 1192 (jury was "instructed that it must find a single conspiracy among [defendant and codefendants] in order to convict [defendant]; it was instructed as to certain characteristics of multiple conspiracies, such as incompatible purposes; and it was told that it must acquit if it found the latter rather than the single conspiracy alleged in the indictment"), Judge Wexler's charge adequately conveyed defendants' theory of defense and the applicable law. The judge's refusal to comply with defendants' request for an instruction that "if you find multiple conspiracies, you must acquit" was not error given the overall import of the charge provided.

b. Proof of a Single Conspiracy

The essence of the crime of conspiracy is the agreement. See, e.g., United States v. Alessi, 638 F.2d at 473. "`[I]n order to prove a single conspiracy, the government must show that each alleged member agreed to participate in what he knew to be a collective venture directed toward a common goal.'" Maldonado-Rivera, 922 F.2d at 963 (citations omitted). The government need not prove that each defendant "knew every other member or was aware of all acts committed in furtherance of" the conspiracy. Alessi, 638 F.2d at 473 (citation omitted). Moreover, "`a single conspiracy is not transposed into a multiple one simply by lapse of time, change in membership, or a shifting emphasis on its locale of operations.'" United States v. Nersesian, 824 F.2d 1294, 1303 (2d Cir.) (quoting Cambindo Valencia, 609 F.2d at 625), cert. denied, 484 U.S. 958, 108 S.Ct. 357, 98 L.Ed.2d 382 (1987). "Finally, a single conspiracy is not transformed into multiple conspiracies merely by virtue of the fact that it may involve two or more phases or spheres of operation, so long as there is sufficient proof of mutual dependence and assistance." Maldonado-Rivera, 922 F.2d at 963.

In this case the evidence offered at trial fit the pattern of the conspiracy alleged in the indictment. The government's two main witnesses. Kryssing and Iorizzo, testified that defendants and other individuals agreed to set up a scheme to avoid paying gasoline excise taxes. They described the efforts of defendants and their co-conspirators to obtain a licensed company through which to "burn" gasoline, efforts that were repeated on at least two other occasions when the previous license became unusable. Other witnesses corroborated their testimony by testifying to defendants' use of specific licenses or "daisy chains" of gasoline transfers to make it appear that taxes had been paid on the gasoline when in fact they had not.

The jury reasonably could have inferred that the different "daisy chains" set up around each license were part of one overall conspiracy. The evidence revealed that once one license became unavailable, defendants searched for another license to further their scheme. Initially defendants utilized Northbrook to make it appear that taxes had been paid on a series of gasoline transfers. When New York cancelled the Northbrook license, defendants began to use the Cabot license to "burn" gasoline. Later, when New York cancelled the Cabot license, the co-conspirators discussed using the Rappaport Fuel and Conlo licenses.

We agree with the government that the use of various "burn" companies here is similar to the conduct in Alessi. In Alessi, defendants were members of a "single loose-knit multi-person conspiracy" to use lost or stolen credit cards to purchase airline tickets for resale at a discounted price. 638 F.2d at 474. Rejecting a claim that the evidence had established a series of smaller, distinct conspiracies rather than the single conspiracy charged, we noted that "[t]he scheme depended for its success on a steady flow of recently stolen or lost cards, since a stolen or lost card may be successfully used for only a short time to unlawfully obtain tickets from airlines." Id. at 470. Likewise, the conspiracy here at all times required a licensed company through which to "burn" gasoline. It was only a matter of time before the IRS or the state recognized that a "burn" company was not paying its tax liability and cancelled the license. When a license no longer was available, the conspirators scrambled to find a replacement license in order to continue the conspiracy.

The instant case also is analogous to United States v. Heinemann, 801 F.2d 86 (2d Cir. 1986), cert. denied, 479 U.S. 1094, 107 S.Ct. 1308, 94 L.Ed.2d 163 (1987), where we upheld convictions for conspiracy to defraud the United States. The Heinemann defendants were charged with conspiring to "impede, impair, obstruct, and defeat the IRS's lawful functions in assessing and collecting revenue, `to wit, the income taxes of themselves and other purported "ministers" of [specific churches] and related "churches."'" 801 F.2d at 91. The conspiracy involved the sale of ministries in purportedly tax-exempt churches. Id. at 88, 91. Because defendants moved from church to church defendants argued that the evidence proved multiple conspiracies involving the sale of ministries in four different churches rather than the single conspiracy charged in the indictment. We rejected this argument because there was ample evidence of a single conspiracy through which the names of churches changed "but the enterprise's goal of avoiding taxes and making money through the sale of ministries" did not. Id. at 92. Likewise, in the instant case there is ample evidence of a single conspiracy through which the name of the companies in a "daisy chain" changed but the conspiracy's goal of avoiding taxes did not.

We are not persuaded by defendants' argument that isolated statements by witnesses that the Cabot "conspiracy" was a separate conspiracy from the Northbrook "conspiracy" are dispositive of the multiple conspiracy issue. The jury reasonably could have inferred based on the evidence as a whole that each license represented a different phase of a single continuing conspiracy. See Maldonado-Rivera, 922 F.2d at 963; see also United States v. Crosby, 294 F.2d 928, 945 (2d Cir. 1961) ("`A single scheme to defraud may involve a multiplicity of ways and means of action and procedure. . . . Mere details may be changed and the scheme remain the same.'") (citation omitted), cert. denied, 368 U.S. 984, 82 S.Ct. 599, 7 L.Ed.2d 523 (1962). As one witness explained, it was "one scheme into another, into another, into another." Defendants did not end one conspiracy and join a new one each time a license became unusable. Instead, they obtained a new license as part of the same fraudulent scheme.

Defendants also point to acrimony among participants in the different phases of the scheme as being inconsistent with a single conspiracy. It appears that Kryssing was responsible, in part, for the cancellation of the Northbrook license, because he "burned" too many gallons of gasoline through the Northbrook license without notifying Iorizzo. Similarly, Iorizzo allegedly caused the cancellation of the Cabot license by "burning" too many gallons of gasoline through it. However, "it is not at all uncommon for disagreements to occur in a common enterprise." Id. Nor is it "inconsistent with such an ongoing, unitary conspiracy that disputes might arise . . . and that switches in affiliation might occur from time to time." Heinemann, 801 F.2d at 92 (footnote omitted); see also Beech-Nut Nutrition Corp., 871 F.2d at 1192 ("`That certain defendants were eager to cheat each other for a large slice of the spoils does not obscure the unifying means used by all of them to defraud the public.'") (citation omitted); Nersesian, 824 F.2d at 1303 ("That conspirators may have problems or difficulties in dealing with one another which result in angry accusations or heated discussions does not necessarily negate the existence of a single conspiracy.") (citation omitted).

Neither does the fact that Kryssing and Iorizzo may have been involved at different phases of the conspiracy depending on which license was being used demonstrate that the evidence established more than one conspiracy. "The jury need not have concluded that the same people were involved throughout the entire period of the conspiracy in order to find one conspiracy." Nersesian, 824 F.2d at 1303.

In sum, there was ample evidence that defendants were involved throughout the different phases of the conspiracy charged and met with various co-conspirators regarding the use of different licenses as circumstances necessitated. The similarities in each of the phases of the conspiracy support a finding that they were part of the same conspiracy, rather than separate conspiracies.

B. Counts Two and Three

Counts Two and Three charge that defendants willfully aided, assisted, procured and caused General and Rappaport Fuel, respectively, to prepare and present to the IRS a fraudulent and false Quarterly Federal Excise Tax Return, Form 720, in violation of IRC section 7206(2). These counts were based on tax returns filed for the first quarter of 1984.

IRC section 7206(2) provides that any person who

[w]illfully aids or assists in, or procures, counsels, or advises the preparation or presentation under, or in connection with any matter arising under, the internal revenue laws, of a return . . . which is fraudulent or is false as to any material matter, whether or not such falsity or fraud is with the knowledge or consent of the person authorized or required to present such return . . . shall be guilty of a felony.

Defendants correctly point out that section 7206(2) is a specific intent statute requiring "willfulness" or "an intentional violation of a known legal duty." United States v. Gurary, 860 F.2d 521, 523 (2d Cir. 1988) (citations omitted), cert. denied, 490 U.S. 1035, 109 S.Ct. 1931, 104 L.Ed.2d 403 (1989); see United States v. Pomponio, 429 U.S. 10, 12, 97 S.Ct. 22, 23, 50 L.Ed.2d 12 (1976) (per curiam). The relevant inquiry on appeal is "whether the Government presented any evidence from which the jury could infer that defendants knew their scheme would result in the filing of false . . . tax returns, and deliberately proceeded with their scheme in the face of that knowledge." Gurary, 860 F.2d at 524; cf. United States v. MacKenzie, 777 F.2d 811, 820 (2d Cir. 1985) ("While appellants had nothing to do with the preparation of the tax returns of the employees in question, they knew the returns would be fraudulently filed and relied on that fact to conceal their ongoing fraud."), cert. denied, 476 U.S. 1169, 106 S.Ct. 2889, 90 L.Ed.2d 977 (1986). The requirements of section 7206(2) have been satisfied.

First, we believe that, viewing the evidence and making all permissible inferences in the light most favorable to the government, there was sufficient evidence from which the jury could find that defendants intended General and Rappaport Fuel to file false or fraudulent tax returns. See Gurary, 860 F.2d at 523-24.

There was evidence that on Kryssing's request Zummo located Cabot, a company with a "clean" license to be purchased by Aracri, Papandon and others. The group purchased Cabot in early 1984 through Zummo and set up Cabot as a sham company. Vestal, which did not have a license, also was formed as a sham company. In accordance with defendants' plan, Cabot purchased gasoline tax-free from Rappaport Fuel and General, which it was able to do because each seller and Cabot possessed licenses. Cabot transferred the gasoline to unlicensed Vestal, representing that taxes had been paid. In fact, no taxes were paid on the gasoline. After that all transfers falsely represented that taxes had been paid: Vestal transferred the gasoline to Petroleum Haulers tax-paid; Petroleum Haulers transferred the gasoline to Pilot or Pride Oil tax-paid. The jury could infer that defendants intentionally structured the transaction in this manner in order to avoid paying taxes on the gasoline.

Where a transaction is a sham for the purpose of avoiding tax liability, the IRS can look behind the form of the transaction to its economic reality. See United States v. Philatelic Leasing Ltd., 794 F.2d 781, 786 (2d Cir. 1986) ("[T]he Government, upon determining that the form employed in a transaction is unreal or a sham, can `sustain or disregard the effect of the fiction as best serves the purposes of the tax statute.'") (quoting Higgins v. Smith, 308 U.S. 473, 477, 60 S.Ct. 355, 357, 84 L.Ed. 406 (1940)). Stripping away the "unreal" transactions flowing through the sham companies, the sales actually were from a licensed company — General or Rappaport Fuel — to Petroleum Haulers, an unlicensed or unregistered company. As a licensed company selling to a non-licensed company, General and Rappaport Fuel actually incurred the tax liability on the sale. However, neither company paid taxes on the transactions and as a result the tax returns of General and those of Rappaport Fuel for the quarter ending March 31, 1984 understated each company's tax liability.

Defendants contend that in order to convict, the jury must have found that they were partners in Cabot and, because the judge refused so to charge the jury, reversal is warranted. Section 7206(2), however, "applies to all knowing participants in the fraud." United States v. Rowlee, 899 F.2d 1275, 1279 (2d Cir.) (citations omitted), cert. denied, ___ U.S. ___, 111 S.Ct. 87, 112 L.Ed.2d 59 (1990). It "make[s] liable any person who willfully attempts to evade payment of either his own tax or that of any other person." 899 F.2d at 1278. "Congress did not intend to exempt anyone from punishment who actively endeavors to defeat a tax, `whatever his relationship to the taxpayer [might] be.'" Id. (citation omitted).

It was not necessary, therefore, for the jury to conclude that defendants were partners in Cabot to find them guilty of Counts Two and Three. Because there was evidence at trial that defendants "attempt[ed] to accomplish the evasion of a tax payment," id., through the use of the Cabot/Vestal scheme they are liable under section 7206(2) regardless of their relationship to General or Rappaport Fuel. Id. at 1278-79. The jury could have inferred that defendants knowingly participated in a complex scheme to avoid paying excise taxes through the use of fictitious invoices and sham companies.

Defendants Aracri and Papandon also contend that we must reverse their convictions on Count Three because no reasonable juror could have concluded that they "caused" Rappaport Fuel to file a fraudulent or false excise tax return. They reason that Rappaport Fuel could not have relied on defendants' actions because Rappaport Fuel knew as of March 1, 1984 that Cabot's license had been revoked on that date and, therefore, Rappaport Fuel knew that it could not legitimately sell gasoline to Cabot tax-free. Rappaport Fuel did not file its quarterly return until late April 1984.

Defendants, however, misconstrue the requirements of section 7206(2). The statute prohibits individuals from willfully aiding, assisting in, procuring, counseling, or advising the preparation or presentation of a fraudulent or false return. Good faith reliance by the taxpayer is not necessary to convict an aider and abettor under this section. See id. at 1279 ("the guilt or innocence of the taxpayer for whom the return was filed is irrelevant to the question of" a section 7206(2) defendant's guilt) (citations omitted); see also 26 U.S.C. § 7206(2) (aider and abettor guilty "whether or not such falsity or fraud is with the knowledge or consent of the person authorized or required to present such return"). It is irrelevant whether Rappaport Fuel knew that it could not legitimately sell gasoline tax-free through Cabot. Such evidence only proves that Rappaport Fuel was a knowing participant in the scheme; it does not relieve defendants of liability.

In sum, we conclude that defendants knew that their scheme would result in the filing of false tax returns. Not only did they proceed with their scheme in spite of this knowledge, the jury reasonably could have inferred that the success of their scheme to avoid the payment of taxes depended on falsely throwing tax liability on a company other than their own. Defendants knew that by purchasing and using Cabot they were creating a fiction to disguise the tax liability on gasoline sold by General and Rappaport Fuel to Petroleum Haulers. Accordingly, we uphold the convictions on Counts Two and Three.

C. Other Claims

We have reviewed defendants' arguments that the district court erred in permitting the government to solicit an opinion from defense's nonexpert summary witness and in admitting portions of a tape recording against defendant Zummo and have found them to be without merit.

D. Nondisclosure of Impeachment Materials

Accordingly, we turn to the allegations that the government failed to turn over impeachment materials and permitted a main government witness to testify falsely. Defendants moved for a retrial after an article in Newsday alerted them to possible impeachment material that the government should have turned over to them before trial. The article, dated February 5, 1991, reported that Iorizzo had been dropped from the Witness Protection Program two years before. Iorizzo told Newsday that he had been thrown out of the program "after program supervisors accused him of crimes, including money laundering and arms trafficking." Sources told Newsday that "Iorizzo was investigated but cleared of the arms-trafficking and money-laundering charges. But they added he had been caught violating other regulations in the program." For example, Iorizzo was suspected of running up $100,000 in credit card bills under an alias.

The government investigated the Newsday allegations and submitted a sealed ex parte summary of its findings to the district court. Judge Wexler denied the motion for a new trial and defendants appeal from that ruling. They ask us to reverse their convictions on two grounds: (1) because Iorizzo testified falsely at trial that he had become a new man after entering into a cooperation agreement with the government in 1984 and the government had information that the testimony was false; and (2) the government improperly did not provide defense with exculpatory material relating to the criminal investigations into Iorizzo's expulsion from the Witness Protection Program despite defense's request for such evidence.

On the eve of oral argument on appeal, the government moved for an adjournment of oral argument and for remand to the district court. Through its motion the government notified us that in the course of preparing for oral argument they had discovered a document that appears to be impeachment material that the government should have disclosed to defense pursuant to Giglio. The government asked us to remand to the district court to determine whether disclosure of the documents likely would have affected the outcome of the trial.

We denied the motion at the time in order to resolve other arguments raised by defendants. Now that we are satisfied that none of defendants' other contentions has merit, we remand to the district court for a determination of whether the material requires reversal of defendants' convictions and a new trial.

CONCLUSION

We affirm defendants' convictions in part and remand to the district court for a determination of whether a new trial is warranted because of the government's nondisclosure of impeachment materials.

APPENDIX