Regularization of Gamma_1-structures in dimension 3

For $Gamma_1$-structures on 3-manifolds, we give a very simple proof of Thurstons regularization theorem, first proved in cite{thurston}, without using Mathers 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.