Relation between the velocity cross (left panel) and auto (right panel) spectra with the density auto-spectrum for the different redshifts and cosmologies considered in this work. The shade of blue represents different values of the total neutrino mass, darker when the neutrino mass is increasing. The various redshifts (z = 0, 0.5, 1, 1.5) are respectively represented with dot-dashed, long dashed, short dashed, and solid lines. The black dotted line represents for each redshift the linear mapping ( and taken in the ΛCDM limit, i.e., at small k).