Canonical Sushi Tokens
List of Sushi Tokens and supporting bridge for farm rewards on the various alternate chains.
Boba BNB & Boba Avax Details
To get SUSHI from ethereum to either boba bnb or boba avax, users will need to bridge to bnb or avalanche first using bridge in above list. Then use boba gateway to move the sushi from specific chain to Boba's rollup for that chain.
Sushi on BSC
Sushi has two tokens on BNB, one that is minted through multichain.org and the other that comes when withdrawing directly from Binance. The multichain.org version is the one used for Sushi Farms, and there is a stable pool supported on Sushi to swap between the two versions.