Though shoehorned into three play-like acts, Birdman transpires in one long, flowing, bravura take — which appears to contain some hidden cuts, à la Hitchcock's Rope, and some CG tricks of the sort that blow the illusion by reminding us we're in a realm where anything's possible so nothing's truly wonderful.
It has less to do with the formal stuntwork — which simulates a single elaborately choreographed take, à la Hitchcock's Rope — than with the unflagging momentum of the performances within it.
The much-vaunted single-take effect achieved by DP Emmanuel Lubezki and editors Douglas Crise and Stephen Mirrione (with a couple of exceptions the film appears to play without cuts ) is not a gimmick, but a storytelling technique that achieves an arguably superior effect to that realized by Alfred Hitchcock in "Rope."
The device was perhaps most famously used by Alfred Hitchcock in his 1948 film, “Rope” (though that film does have several hard cuts between reels), and in Alexander Sokurov’s 2002 fantasy, “Russian Ark.”
What isn't in doubt is the fantastic cinematography courtesy of DP Emmanuel Lubezki who employs a near continuous shot throughout the film (with an unknown amount of actual cuts -- presumably across dark scenes much like Alfred Hitchcock used in the somewhat similarly shot "Rope" but likely also elsewhere now that visual effects can be used to create the appearance of seamlessness).
Though it wouldn’t be accurate to say Birdman was filmed in a single long take—there are several moments when characters pass through a darkened space in order to mask visible cuts, the digital-age equivalent of the reel changes in Rope —Iñárritu and Lubezki go to great lengths to make sure the film feels to the viewer like one continuous shot.