1. A computer program product for facilitating processing in a computing environment, said computer program product comprising: a computer readable storage medium readable by a processing circuit and storing instructions for execution by the processing circuit for performing a 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; updating the tracking set assigned to the transaction based on the determining indicating the tracking set assigned to the transaction is to be update; and wherein the request includes a read access and the determining whether the tracking set to be used to track cache accesses is to be updated comprises determining whether one or more other write sets of at least the selected portion of the cache is marked by one or more transactions other than the transaction issuing the request, and wherein the updating the tracking set assigned to the transaction is performed based on the one or more other write sets being unmarked, wherein the updating the tracking set includes updating the read set of the tracking set.