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This is explained by Zangetsu when he is first introduced: Shinigami can fix the spirit particles in the air around them underneath their feet and use it to land and stand on. Doing this is second nature to most high level Shinigami, to the point of being almost subconsciously done. They use a technique called Shunpo to move quickly from one point to another.

"they also walk on invisible bridges created by sushimaru" -kon

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