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In this paper, the design of irregular turbo codes for the binary erasure channel is investigated. An analytic expression of the erasure probability of punctured recursive systematic convolutional codes is derived. This expression will be used to study the density evolution of turbo codes over the binary erasure channel, that will allow for the design of capacity-approaching irregular turbo codes. Next, we propose a graph-optimal interleaver for irregular turbo codes. Simulation results for different coding rates are shown at the end.