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We consider the design of a P2P network for the distribution of real-time video streams through the Internet. We follow a multi-source approach where the stream is decomposed into several flows sent by different peers to each client. The goal is to resist to the frequent moves of the peers entering and leaving the network. We analyze our approach using the recently proposed PSQA technology which allows to obtain an accurate (and automatic) numerical evaluation of the quality as perceived by each client. Our transmission technique includes the use of an arbitrary amount of redundancy in the signal, whose specification is a part of the dimensioning process, and it works with very low signaling overhead. We illustrate with real data how the overall system allows to compensate efficiently the possible losses of frames due to peers leaving the network.