The Extreme Energy Event (EEE) experiment is devoted to the search of high energy cosmic rays through a network of telescopes installed in about 50 high schools distributed throughout the Italian territory. This project requires a peculiar data management infrastructure to collect data registered in stations very far from each other and to allow a coordinated analysis. Such an infrastructure is realized at INFN-CNAF, which operates a Cloud facility based on the OpenStack opensource Cloud framework and provides Infrastructure as a Service (IaaS) for its users. In 2014 EEE started to use it for collecting, monitoring and reconstructing the data acquired in all the EEE stations. For the synchronization between the stations and the INFN-CNAF infrastructure we used BitTorrent Sync, a free peer-to-peer software designed to optimize data syncronization between distributed nodes. All data folders are syncronized with the central repository in real time to allow an immediate reconstruction of the data and their publication in a monitoring webpage. We present the architecture and the functionalities of this data management system that provides a flexible environment for the specific needs of the EEE project.