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 that are accessed by a host application on a host device, the method comprising: mapping application address space to address space on the host device containing metadata for the target device and providing additional local metadata therefor on the host device; replacing within the application the address of metadata for the source device with the address of metadata for the target device; migrating the data from the source device to the target device; setting a diversion flag that is part of the additional local metadata, wherein the diversion flag indicates a remapping of extents; maintaining the diversion flag in a set state while the data set at the source device is open; and closing and unallocating the data set at the source device.