An asset trading on many exchanges has no mechanism forcing those venues to agree on a price. They stay aligned because divergence is profitable to remove, and that profit attracts people who remove it.
Each venue has its own independent book
Every exchange matches its own orders against its own resting liquidity, and nothing connects one book to another.
A large buy on one venue moves only that venue's price, leaving the same asset temporarily cheaper elsewhere.
Without intervention those prices would drift apart indefinitely, since neither book has any information about the other.
The trade is simultaneous and directionless
An arbitrageur buys where the asset is cheap and sells where it is expensive at the same moment, ending with the same net exposure as before.
The profit is the difference between the two prices, less fees and transfer costs, and it does not depend on which way the market subsequently moves.
Buying pressure on the cheap venue and selling pressure on the expensive one push the two prices together automatically.
Inventory replaces transfers
Moving assets between exchanges takes time and confirmations, which is far too slow to capture a difference that lasts seconds.
Active participants therefore hold balances on every venue they trade, so both legs execute immediately without anything crossing a chain.
Positions are rebalanced periodically rather than per trade, which turns capital allocation into the real constraint on how much arbitrage capacity exists.
Holding balances across many venues also means accepting the risk of each one, so the business is partly a judgement about which exchanges will still honour a withdrawal request next week.
Persistent gaps indicate a barrier
Where a price difference lasts, something is preventing the trade rather than nobody having noticed it.
Withdrawal suspensions, restricted market access, currency controls and unreliable settlement all stop capital from moving to where it would be used.
Regional premiums and discounts are the visible form of this, and they reflect the difficulty of moving money rather than a disagreement about value.
On-chain venues are arbitraged differently
Automated market makers price from their reserves alone, so they do not update when centralised markets move, and the gap is closed by someone trading against the pool.
That correction is competitive and public, since the pending transactions are visible before they execute and others can attempt to act first.
Liquidity providers absorb the cost of those corrections, which is a real component of what supplying a pool actually earns.