  We perform numerical simulations of the Sivers effect from single spin
asymmetries in Drell-Yan processes on transversely polarized protons. We
consider colliding antiprotons and pions at different kinematic conditions of
interest for the future planned experiments. We conventionally name "framework
I" the results obtained when properly accounting for the various flavor
dependent polarized valence contributions in the numerator of the asymmetry,
and for the unpolarized nonvalence contribution in its denominator. We name
"framework II" the results obtained when taking a suitable flavor average of
the valence contributions and neglecting the nonvalence ones. We compare the
two methods, also with respect to the input parametrization of the Sivers
function which is extracted from data with approximations sometimes
intermediate between frameworks I and II. Deviations between the two approaches
are found to be small except for dilepton masses below 3 GeV. The Sivers effect
is used as a test case; the arguments can be generalized to other interesting
azimuthal asymmetries in Drell-Yan processes, such as the Boer-Mulders effect.
