  We discuss transversity distributions and Drell-Yan transverse double spin
asymmetries. First, the antiquark flavor asymmetry $\Delta_{_T} \bar
u/\Delta_{_T} \bar d$ is discussed by using two different descriptions, a
meson-cloud model and a Pauli exclusion model. We find that both calculations
produce a significant $\Delta_{_T} \bar d$ excess over $\Delta_{_T} \bar u$.
Next, we study its effects on the transverse spin asymmetry $A_{_{TT}}$ and on
the Drell-Yan proton-deuteron asymmetry $\Delta_{_T}\sigma^{pd}/2
\Delta_{_T}\sigma^{pp}$. We find that the ratio $\Delta_{_T}\sigma^{pd}/2
\Delta_{_T}\sigma^{pp}$ is very useful for investigating the flavor asymmetry
effect.
