Regularization of Gamma₁-structures in dimension 3

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For Γ₁-structures on 3-manifolds, we give a very simple proof of Thurston's regularization theorem, first proved in thurston, without using Mather's homology equivalence. Moreover, in the co-orientable case, the resulting foliation can be chosen of a precise kind, namely an "open book foliation modified by suspension." There is also a model in the non co-orientable case.