In this talk, I will discuss results obtained with Yvan Dynnikov, Paul Mercat, Olga Paris-Romaskevich and Sasha Skripchenko. Novikov's conjecture for foliations states that the restriction of a linear foliation to a triply periodic surface is generically periodic or integrable (leaves stay at bounded distance from a line). I will explain some results on families of interval exchange transformations with flips. This approach gives a partial solution to the conjecture in a non-trivial case.