From the Super Mario Wiki
Flutter Wings are power-ups that first appeared in Yoshi's New Island. It has a similar effect to the Invincibility Leaf from Super Mario 3D Land, meaning that it only appears after Yoshi loses three lives in a level. Mr. Pipe gives Yoshi this power-up and grants him flight. The flight is different to that of the Invincibility Leaf, in that it allows Yoshi to hover, not glide, and stay at a mostly constant height. There is a variation of Flutter Wings called Golden Flutter Wings, which acts more like an Invincibility Leaf and are only used When Yoshi loses another life with the Flutter Wings. If all the levels are completed without the Flutter Wings, then there will be a battle with Bowser before Baby Luigi and the Stork are saved.
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