@Jennifer5138 it is not allowed to transfer the Airbnb account from the seller to the purchaser. If you have circumvented this rule then Airbnb will not know anything other than passing the earnings info to you.
If however you started a new listing as per the rules then only your income should be taxable by you.
Finally if its a registered business that you have bought then any tax liabilities should have been sorted out in the purchase contract.