From Sherwood v. Marquette Transp. Co., 2009 U.S. App. LEXIS 25581 (7th Cir. 2009):

This leads Bluegrass Marine to invoke the collateral-order doctrine. See Cohen v. Beneficial Industrial Loan Corp., 337 U.S. 541, 69 S. Ct. 1221, 93 L. Ed. 1528 (1949). The last decision treating the denial of a stay as an appealable collateral order came in 1988, and there is a good reason for recent silence. The Supreme Court has held that a district judge's refusal to stay, dismiss, or transfer a case under a forum-selection clause is not appealable as a collateral order, because the issue can be resolved on appeal from the final decision. See Lauro Lines s.r.l. v. Chasser, 490 U.S. 495, 109 S. Ct. 1976, 104 L. Ed. 2d 548 (1989). See also Digital Equipment Corp. v. Desktop Direct, Inc., 511 U.S. 863, 114 S. Ct. 1992, 128 L. Ed. 2d 842 (1994) (refusal to stay or dismiss a suit under a settlement contract is not appealable as a collateral order); Van Cauwenberghe v. Biard, 486 U.S. 517, 108 S. Ct. 1945, 100 L. Ed. 2d 517 (1988) (refusal to stay, dismiss, or transfer a suit in response to an assertion of forum non conveniens is not appealable as a collateral order). An arbitration agreement is a specialized forum-selection clause. See Vimar Seguros y Reaseguros, S.A. v. M/V Sky Reefer, 515 U.S. 528, 115 S. Ct. 2322, 132 L. Ed. 2d 462 (1995); Rodriguez de Quijas v. Shearson/American Express, Inc., 490 U.S. 477, 109 S. Ct. 1917, 104 L. Ed. 2d 526 (1989). It follows that a district judge's decision to proceed with the suit is not a "final decision" immediately appealable under 28 U.S.C. § 1291. See Wabtec Corp. v. Faiveley Transport Malmo AB, 525 F.3d 135, 138 (2d Cir. 2008).

Bluegrass Marine also maintains that the district court's order is appealable under 28 U.S.C. § 1292 as the denial of an injunction. An old line of cases supports that position, but "old" is a vital qualifier. An equation between denials of stays and injunctions reflected the Enelow-Ettelson doctrine, which was overruled in Gulfstream Aerospace Corp. v. Mayacamas Corp., 485 U.S. 271, 108 S. Ct. 1133, 99 L. Ed. 2d 296 (1988). Doubtless it is possible for a district judge's procedural order to be treated as the denial of an injunction when it postpones resolution of the dispute and causes the same sort of irreparable injury as the denial of an interlocutory injunction would do. Gulfstream Aerospace itself said as much. Perhaps this is what McNamara v. Yellow Transportation, Inc., 570 F.3d 950 (8th Cir. 2009), meant when stating that a refusal to stay a suit may be appealed under § 1292(a)(1). But Sherwood's suit seeks damages, not an injunction; thus the choice between resolving the dispute in court or before an arbitrator could not grant or deny an injunction.

If the Eighth Circuit believes that every anti-arbitration order is appealable as an injunction, it is at odds with this circuit and many others. See Briggs & Stratton Corp. v. Industrial Workers Union, 36 F.3d 712, 714 (7th Cir. 1994) (disagreeing with Nordin v. Nutri/System, Inc., 897 F.2d 339 (8th Cir. 1990), the sole decision on which McNamara relied); Central States Pension Fund v. Central Cartage Co., 84 F.3d 988 (7th Cir. 1996). Section 16 [of the FAA] supplied appellate jurisdiction in McNamara; that court's invocation of § 1292(a)(1) was unnecessary as well as imprudent, for the reasons Briggs & Stratton develops.