various EoS during the hydrodynamic evolution and with the pure cascade calculations within the same framework.

It is well-known that by using HBT interferometry techniques one can get detailed information about the space-time configuration of the system at freeze-out. We concentrate here on the two (identical) pion interferometry and test the sensitivity of the HBT results on different stages of the evolution. In our previous investigations on the HBT correlation of various identical particle pairs from HICs at AGS, SPS, and RHIC energies [@Li:2006gp; @Li:2006gb; @Li:2007im; @Li:2007yd; @Li:2008ge; @Li:2008bk], we adopted the UrQMD model but further considered the mean field potentials for both confined and “pre-formed” particles in the model [@Li:2007yd; @Li:2008ge; @Li:2008bk]. We found that also initial stage interaction may contribute to a better description of the HBT time-related puzzle throughout the energies from AGS, SPS, up to RHIC.

In this paper we perform a systematic investigation of the sensitivity of HBT correlation of negatively charged pions to the EoS by applying the newly developed hybrid approach. Similar more focused studies were frequently discussed with microscopic transport or hydrodynamic models before [@Rischke:1996em; @Soff:2000eh; @Zschiesche:2001dx; @Lisa:2005dd]. It is also interesting to study if the current set of EoS employed in 