  A systematic study of HBT radii of pions, produced in heavy ion collisions in
the intermediate energy regime (SPS), from an integrated (3+1)d
Boltzmann+hydrodynamics approach is presented. The calculations in this hybrid
approach, incorporating an hydrodynamic stage into the Ultra-relativistic
Quantum Molecular Dynamics transport model, allow for a comparison of different
equations of state retaining the same initial conditions and final freeze-out.
The results are also compared to the pure cascade transport model calculations
in the context of the available data. Furthermore, the effect of different
treatments of the hydrodynamic freeze-out procedure on the HBT radii are
investigated. It is found that the HBT radii are essentially insensitive to the
details of the freeze-out prescription as long as the final hadronic
interactions in the cascade are taken into account. The HBT radii $R_L$ and
$R_O$ and the $R_O/R_S$ ratio are sensitive to the EoS that is employed during
the hydrodynamic evolution. We conclude that the increased lifetime in case of
a phase transition to a QGP (via a Bag Model equation of state) is not
supported by the available data.
