We calculate the gauge invariant Drell-Yan-like hadron tensors. In connection with new COMPASS results, we predict the new single spin asymmetry which probes gluon poles together with chiral-odd and time-odd functions. The relevant pion production as a particular case of the Drell-Yan-like process has been discussed. For the meson-induced Drell-Yan (DY) process, we model an analog of the twist-3 distribution function, which is a collinear function in inclusive channel, by means of two noncollinear distribution amplitudes which are associated with exclusive channel. This modeling demonstrates the fundamental duality between different factorization regimes.