  An integrated Boltzmann+hydrodynamics transport approach is applied to
investigate the dependence of the mean transverse mass on the freeze-out and
the equation of state over the energy range from $E_{\rm lab}=2-160A $GeV. This
transport approach based on the Ultra-relativistic Quantum Molecular Dynamics
(UrQMD) with an intermediate hydrodynamic stage allows for a systematic
comparison without adjusting parameters. We find that the multiplicities of
pions and protons are rather insensitive to different freeze-out prescriptions
and changes in the equation of state, but the yields are slightly reduced in
the hybrid model calculation compared to a pure transport calculation while the
(anti)kaon multiplicities are increased. The mean transverse mass excitation
functions of all three particle species are found to be sensitive to the
different freeze-out treatments as well as to the equation of state. We find
that the bag model equation of state with a strong first order phase transition
is in qualitative agreement with the experimentally observed step-like
behaviour in the < m_T > excitation function. The hybrid model with a hadron
gas equation of state leads to a overestimation of the < m_T >, especially at
higher energies. However, non-equilibrium effects seem also to be substantial
as is suggested by the comparison with standard UrQMD results.
