Indefinite Owl Flight is a glitch which allows Mario to use Hoot to go upward indefinitely. To perform the glitch, Mario must let go of Hoot, pause the game before losing too much height, wait 30 frames, and then unpause the game. After unpausing Mario will grab onto Hoot again, bypassing the normal cooldown time that normally occurs when Mario lets go and allowing him to fly up with Hoot indefinitely. The glitch occurs because the game determines whether sufficient time has passed for Mario to regrab Hoot by comparing the value of the global timer when Mario let go of Hoot with the current value of the global timer. Since the global timer increments when the game is paused, pausing during the cooldown period lets Mario regrab Hoot without losing height. This glitch can be utilized to enter a vertical parallel universe.
Video of the glitch
Using the glitch to reach a Vertical PU (Epilepsy Warning)