The oxygen content of sea water is a major factor affecting marine fauna and biogeochemical cycles. Zones were an oxygen deficit is present in the water column represent significant portions of the total area and volume of the world's oceans and are thought to be increasing. In the Eastern Tropical Pacific an oxygen minimum zone is found, maintained primarily by biological processes and weak ventilation and where equatorial and eastern boundary current systems drive the circulation. The Eastern Tropical Pacific Oxygen Minimum Zone developed off Peru is populated by mesoscale eddies whose role on the exchange of water mass properties remains largely unknown. We study this problem from a modeling approach and a Lagrangian point of view, characterizing pathways and barriers to transport and mixing of oceanic regions with distinct concentrations of dissolved oxygen. Our results show the crucial role of mesoscale dynamics in the establishment of the Oxygen Minimum Zone.