1. A method of providing mobility to virtual storage processors (VSPs), the method comprising: operating a source VSP on a physical storage processor, the physical storage processor having a first network address, the source VSP having a second network address different from the first network address and providing host access to multiple source data objects via the second network address; receiving, by processing circuitry, a VSP move command from a user, the VSP move command specifying the source VSP and a destination; identifying, by the processing circuitry and in response to the VSP move command, the multiple source data objects which are configured to store data from the context of the source VSP, the multiple source data objects residing in a source storage pool; and after the multiple source data objects are identified, (i) transforming the multiple source data objects into multiple destination data objects which are configured to store data from the context of a destination VSP at the destination, the multiple destination data objects residing in a destination storage pool which is different from the source storage pool, and (ii) providing host access to the multiple source data objects, residing in the destination storage pool, via the second network address, wherein the physical storage processor on which the source VSP operated is a first physical storage processor, wherein the destination VSP resides on a second physical storage processor having a third network address, and wherein the third network address is different from the first network address and the second network address.