Maintaining multiple target copies

Provided are techniques for maintaining instant virtual copies. A request to perform an instant virtual copy operation to create an instant virtual copy from a first volume to a new volume is received. It is determined that the first volume has not been modified since a last instant virtual copy operation has been performed. It is determined whether an intermediate volume and an intermediate map have already been created. In response to determining that the intermediate volume and the intermediate map have not already been created, the intermediate volume and the intermediate map are created, the intermediate volume is made dependent on the first volume in a dependency chain based on the intermediate map, and the new volume is made dependent on the intermediate volume in the dependency chain.