Collins and Sivers Asymmetries from COMPASS

In the years 2002-2004 the COMPASS experiment has collected data with a polarized LiD target and a 160 GeV muon beam. About 20% of the running time has been devoted to measure transverse spin effects in semi inclusive deep inelastic scattering, one of the main objectives of the COMPASS spin program. The results for the Collins and the Sivers asymmetries, both for unidentified and identified hadrons, are presented here. The measured asymmetries on the LiD target are small and compatible with zero within the few percent statistical errors, an important result which can be interpreted as cancellation between u and d quark contribution in the deuteron and which allows to better constrain the parton distribution functions.