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Scientific workflow systems are numerous and equipped of provenance modules able to collect data produced and consumed during workflow runs to enhance reproducibility. An increasing number of approaches have been developed to help managing provenance information. Some of them are able to process data in a polynomial time but they require workflows to have series-parallel (SP) structures. Rewriting any workflow into an SP workflow is thus particularly important. In this paper, (i) we introduce the concept of provenance-equivalent rewriting process, (ii) we review existing graph transformations, (iii) we design the provenance-equivalent SPFlow algorithm, (iv) we evaluate our approach over a thousand of real workflows.