We apply an inverse model to a hydrographic cruise that completely closes the Canary Islands to investigate their effect on the water masses transports. Most central waters are transported south between the eastern islands and the African coast, with 2.5 Sv out of a total of 3.5 Sv. Intermediate waters are effectively blocked by the islands passages, with Mediterranean/Antarctic waters predominantly found north/south of the islands, and most deep waters loop around the archipelago plateau. A process model upholds the existence of intense two-way exchange between central and intermediate waters along the eastern passage, with vertical velocities of order 10-5 m s-1.