We have developed an event-by-event relativistic kinetic transport approach to study the build up of the anisotropic flows v n ( p T ) for a system at fixed η / s ( T ) . The partonic approach describe the evolution of massless partons which imply ϵ = 3 p as Equation of State (EoS). We extend previous studies to finite partonic masses tuned to simulate a system that expand with an EoS close to the recent lQCD results. We study the role of EoS and the effect of η / s ( T ) ratio on the build up of v n ( p T ) up to n = 5 for two beam energies: RHIC energies at s = 200  GeV and LHC energies at s = 2.76  TeV. We find that for the two beam energies considered the suppression of the v n ( p T ) due to the viscosity of the medium have different contributions coming from the cross over or QGP phase. We shows that in ultra-central collisions (0–0.2%) the v n ( p T ) have a stronger sensitivity to the T dependence of η / s that increases with the order of the harmonic n. Finally, we discuss the results for the integrated flow harmonics ⟨ v n ⟩ in ultra-central collisions pointing-out how the relative strength of ⟨ v n ⟩ depend on the colliding energies as well as on the freeze-out dynamics.