  We estimate the single-spin asymmetries (SSA) which provide the access to
transversity as well as to Boer-Mulders and Sivers PDFs via investigation of
the single-polarized Drell-Yan (DY) processes with $ pp$, $pD$ and $DD$
collisions available to RHIC, NICA, COMPASS, and J-PARC. The feasibility of
these SSA is studied with the new generator of polarized DY events. The
performed estimations demonstrate that there exist the such kinematical regions
where SSA are presumably measurable. The most useful for PDFs extraction are
the limiting kinematical ranges, where one can neglect the sea PDFs
contributions which occur at large values of Bjorken x. It is of interest that
on the contrary to the Sivers PDF, the transversity PDF is presumably
accessible only in the especial kinematical region. On the contrary to the
option with the symmetric collider mode (RHIC, NICA), this is of importance for
the COMPASS experiment and the future J-PARC facility where the fixed target
mode is available.
