Non-identical particle femtoscopy probes not only the size of the emitting system, but also the emission asymmetries between particles of different mass, which are intimately related with the collective behavior of matter. We apply the technique to the simulations from the THERMINATOR+Lhyquid model of the heavy-ion collisions at √ sNN = 200 GeV. We present predictions for all pairwise combinations of pions, kaons, and protons, and discuss their interpretation. We show that kaon and proton distributions are strongly influenced by flow: the source gets smaller and shifted to the outside with growing pT , while for pions the shift is significantly smaller, producing an emission asymmetry. We explain how particles coming from decays of hadronic resonances enhance the asymmetry signal coming from flow, contrary to naive expectations. Emphasis is put on extracting this unique information about collective behavior of matter from the non-identical particle correlations. We also present, in detail, the technical aspects of the non-identical particle femtoscopy technique applied to data from the heavy-ion collisions. We list the sources of systematic errors coming from the method itself and the usual assumptions. We describe robust analysis methods and discuss their limitations.