Embodiments of the invention relate to creating and maintaining consistent data sets in a shared pool of configurable computer resources to support disaster recovery support. Data from an application is stored in local data storage and replicated to another data storage. A consistency point of the data is created in both of the data storage, with the consistency point representing an identical data set at a point-in-time. Based upon the created consistency points, a consistent set of application data may be requested to support a read operation for a migrated application.