1. A computer-implemented method of facilitating processing in a computing environment, said computer-implemented method comprising: obtaining, from a transaction executing on a processor of the computing environment, a request to access a cache of the computing environment; determining, based on obtaining the request, whether a tracking set to be used to track cache accesses is to be updated, the tracking set comprising a read set to track read accesses of at least a selected portion of the cache and a write set to track write accesses of at least the selected portion of the cache, the tracking set being assigned to the transaction, wherein another transaction to access the cache has another tracking set assigned thereto; and updating the tracking set assigned to the transaction based on the determining indicating the tracking set assigned to the transaction is to be updated.