Described are techniques for use with online data copying or migration. Data is pushed from a source to a target device while one or both of the source and target devices are available for use by one or more host systems. The host systems may perform I/O operations to the source and/or target devices while the data migration is ongoing if a copy session is defined on the data storage system(s) of the source and/or target devices. A copying operation performs data migration from the source to the target device. A migration vector is used to indicate which portions of the source have been migrated. A change vector may be associated with each of the source and/or target devices to indicate portions that have been modified in order to perform a differential copy operation.