  Transverse-mass spectra, their inverse slopes and mean transverse masses in
relativistic collisions of heavy nuclei are analyzed in a wide range of
incident energies 2.7 GeV $\le \sqrt{s_{NN}}\le$ 39 GeV. The analysis is
performed within the three-fluid model employing three different equations of
state (EoS's): a purely hadronic EoS, an EoS with the first-order phase
transition and that with a smooth crossover transition into deconfined state.
Calculations show that inverse slopes and mean transverse masses of all the
species (with the exception of antibaryons within the hadronic scenario)
exhibit a step-like behavior similar to that observed for mesons and protons in
available experimental data. This step-like behavior takes place for all
considered EoS's and results from the freeze-out dynamics rather than is a
signal of the deconfinement transition. A good reproduction of experimental
inverse slopes and mean transverse masses for light species (up to proton) is
achieved within all the considered scenarios. The freeze-out parameters are
precisely the same as those used for reproduction of particles yields in
previous papers of this series. This became possible because the freeze-out
stage is not completely equilibrium.
