Each canonical FRAX/FXS ERC20 token contract has a 1 to 1 stableswap AMM built into the token which allows swapping to/from the canonical FRAX/FXS of the network for any supported bridged FRAX/FXS. This allows tight arbitrage of the FRAX peg and also maintains the single distribution of FXS across all chains. For example, let's assume that canonical FRAX on Fantom is $.990. An arbitrager can purchase as much canonical FRAX as possible at $.990 knowing that she can swap them 1 to 1 for anyFRAX in the stableswap pool within the ERC20 token contract then bridge the anyFRAX back to ETH mainnet (or any other chain) where FRAX is at peg to make a profit.
Therefore, purchasing canonical FRAX/FXS on one chain is the same as purchasing FRAX/FXS on another chain. If you bridge FRAX/FXS using any of the supported bridges (more to be added soon), you can swap the bridged token for native FRAX/FXS on that chain to farm/LP/hold etc. Additionally, when canonical FRAX/FXS is minted with AMOs on any chain, the protocol checks that there is enough swap liquidity available with the token contract to move canonical tokens across chains so that the peg is always global and arbitraged.