Here we analyze the dispersion behavior of revolver-type anti-resonant hollow core fibers, revealing that the chromatic dispersion of this type of fiber geometry is dominated by the resonances of the glass annuluses, whereas the actual arrangement of the anti-resonant microstructure has a minor impact. Based on these findings we show that the dispersion behavior of the fundamental core mode can be approximated by that of a tube-type fiber, allowing us to derive analytic expressions for phase index, group-velocity dispersion and zero-dispersion wavelength. The resulting equations and simulations reveal that the emergence of zero group velocity dispersion in anti-resonant fibers is fundamentally associated with the adjacent annulus resonance which can be adjusted mainly via the glass thickness of the anti-resonant elements. Due to their generality and the straightforward applicability our findings will find application in all fields addressing controlling and engineering of pulse dispersion in anti-resonant hollow core fibers.