Predictions for the single transverse spin asymmetry AN in semi-inclusive DIS processes are given; non-negligible values of AN may arise from spin effects in the fragmentation of a polarized quark into a final hadron with a transverse momentum ěc k⊥ with respect to the jet axis, the so-called Collins effect. The elementary single spin asymmetry of the fragmenting quark has been fixed in a previous paper, by fitting data on parrow p -> π X, and by assuming that the QCD factorization theorem holds also when transverse momenta are taken into account. The predictions given here are based on the assumption that the Collins effect is the only cause of the observed single spin asymmetries in parrow p -> π X. Eventual spin and ěc k⊥ dependences in the quark distribution functions, the so-called Sivers effect, are also discussed.