  COMPASS is a fixed target experiment at the CERN SPS, with a rich physics
program focused on nucleon spin structure and on hadron spectroscopy. One of
the main goals of the spin program is the measurement of the transverse spin
distribution function $\Delta_T q(x)$ in semi-inclusive DIS off transversely
polarized nucleons. For this purpose approximately 20% of the running time in
the years 2002 to 2004 with the longitudinally polarized muon beam of 160 GeV
and with $^6$LiD polarized target was used to collect data with the target
polarized transversely with respect to the beam direction. The 2002 data have
been already analysed and published. We present here the preliminary results
from the full statistics for the Collins and Sivers single hadron asymmetries
and for the transverse spin asymmetry in hadron pair production.
