1. A method of releasing a data set at a source device in connection with migrating data from the source device to a target device, the method comprising: mapping application address space to address space containing metadata for the target device and providing additional local metadata therefor; migrating the data from the source device to the target device; replacing within the application the address of metadata for the source device with the address of metadata for the target device; setting a diversion flag that is part of the additional local metadata, wherein the diversion flag indicates a remapping of extents, wherein, before replacing within the application the address of metadata for the source device with the address of metadata for the target device, input/output (I/O) operations of the application are diverted from the source device to the target device based on the diversion flag without disrupting the application, wherein the diversion flag is located in a data structure provided with private address space storage of the application that is mapped to a host memory page corresponding to the data that allows the diversion flag of the data structure to be located when the data is referenced, and wherein, after migrating the data and after replacing within the application the address of metadata for the source device with the address of metadata for the target device, the diversion flag is cleared and the data set at the source device is released without the application having to terminate; and closing and unallocating the data set at the source device, wherein the closing and unallocating of the data set are performed without the application having to terminate, and wherein memory space at the source device used for the data set is made available for reuse without the application having to terminate.