From the Super Mario Wiki
Super Mario 3D Land
In Super Mario 3D Land, it only appears after Mario loses five lives in a level that is not already completed. It will not appear when re-visiting a completed level or a Special World level. This means Luigi cannot obtain it in that game unless the player skipped any levels in the normal worlds (for example, by using a Warp Zone). Touching it will give Mario a shining white and golden Tanooki Suit, making him White Tanooki Mario, and it will make him invincible, as the Star also does, but the invincibility lasts for the entire level. After completing a level with it, the player will revert back to the normal Tanooki form. The Invincibility Leaf however does not protect Mario from lava or an abyss.
New Super Mario Bros. 2
The Invincibility Leaf returns in New Super Mario Bros. 2, but changes Mario into White Raccoon Mario instead of White Tanooki Mario. As with Super Mario 3D Land, one only appears after Mario loses five consecutive lives in any given level, with the exception of the Cannon levels. As White Raccoon Mario, the Power Meter fills up faster than as normal Raccoon Mario, and Mario has the ability to walk/run on water, like Mini Mario. The power-up will last for the entire level and will revert to normal Raccoon Mario/Luigi upon completion. Its Assist Block will remain in the level until the player beats it without using it. It can also be used in Coin Rush mode, where Mario remains in White Raccoon form for the entire pack.
The Invincibility Leaf cannot be replaced by any power-up items, including the Gold Flower and Mega Mushroom. However, the Star item can still be used while the Invincibility Leaf is in effect. To obtain the secret exits and unlock hidden levels, the player must clear the level without using the Invincibility Leaf.
However, unlike Super Mario 3D Land, the Invincibility Leaf will show up in a level, providing Mario or Luigi have met the criteria of losing five lives, regardless of whether or not the level in question has been cleared. This means Luigi can be a White Fox at any level, as opposed to 3D Land.
Super Mario 3D World
The Invincibility Leaf also appears in Super Mario 3D World, referred to as the Invincible Super Leaf on the website. It functions the same way as in Super Mario 3D Land.
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