  We examine in detail the diagrammatic mechanisms which provide the change of
sign between the single transverse spin asymmetries measured in semi-inclusive
deep inelastic scattering (SIDIS) and in the Drell-Yan process (DY). This
asymmetry is known to arise due to the transverse spin dependence of the target
proton combined with a T-odd complex phase. Using the discrete symmetry
properties of transverse spinors, we show that the required complex phase
originates in the denominators of rescattering diagrams and their respective
cuts. For simplicity, we work in a model where the proton consists of a valence
quark and a scalar diquark. We then show that the phases generated in SIDIS and
in DY originate from distinctly different cuts in the amplitudes, which at
first appears to obscure the relationship between the single-spin asymmetries
in the two processes. Nevertheless, further analysis demonstrates that the
contributions of these cuts are identical in the leading-twist Bjorken
kinematics considered, resulting in the standard sign-flip relation between the
Sivers functions in SIDIS and DY. Physically, this fundamental, but yet
untested, prediction occurs because the Sivers effect in the Drell-Yan reaction
is modified by the initial-state "lensing" interactions of the annihilating
antiquark, in contrast to the final-state lensing which produces the Sivers
effect in deep inelastic scattering.
