In order to better identify the role of the magnetic topology on ITG and TEM instabilities, different MHD equilibria with increasing complexity are calculated using the CHEASE code [1]. We start from the geometry of the s-alpha cyclone benchmark case [2], consider the corresponding circular numerical equilibrium, and then successively add a non zero value of alpha consistent with the kinetic profiles, an elongation of 1.68, a triangularity of 0.15, and finally an up-down asymmetry corresponding to a single-null diverted geometry. This gives the opportunity to study separately the effect of each main characteristics of the equilibrium on microinstabilities in core plasmas. Linear local electrostatic gyrokinetic simulations of these different numerical equilibria and of their corresponding analytical descriptions (Miller-type representations [3]) are performed using the codes GS2 [4, 5] and GYRO[6]. It is observed that each modification of the equilibrium has an influence on the results of gyrokinetic simulations. The effect of the alpha parameter can compensate the stabilizing effect of an increase in the elongation. A comparison between the up-down symmetric shaped equilibrium and its corresponding diverted configuration show a non negligible effect on the growth rate of ITG and TEM turbulence. The comparison between the local Miller model and using a full equilibrium shows that it is mainly the indirect change of elongation in the plasma core which influences the results. The global aim is to provide well defined benchmark cases including real geometry and kinetic electrons physics, since this is not analyzed by the cyclone case. In addition, the goal is to define a procedure for testing of local simulations inspired by experimental constraints and results.