  Double pants decompositions were introduced in our paper "Double pants
decompositions of 2-surfaces" (Mosc. Math. J. 11 (2011), no. 2, 231-258,
arXiv:1005.0073), together with a flip-twist groupoid acting on these
decompositions. It was shown that flip-twist groupoid acts transitively on a
certain topological class of the decompositions, however, recently Randich
discovered a serious mistake in the proof. In this note we present a new proof
of the result, accessible without reading the initial paper.
