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In the literature different approaches have been proposed to compute the anisotropies of the astrophysical gravitational wave background. The different expressions derived, although starting from our work [Cusin, Pitrou, Uzan, Phys. Rev. D 96, 103019 (2017)PRVDAQ2470-001010.1103/PhysRevD.96.103019], seem to differ. This article compares the various theoretical expressions proposed so far and provides a separate derivation based on a Boltzmann approach. We show that all the theoretical formula in the literature are equivalent and boil down to the one of [Phys. Rev. D 96, 103019 (2017)PRVDAQ2470-001010.1103/PhysRevD.96.103019] when a proper matching of terms and integration by parts are performed. The difference between the various predictions presented for anisotropies in a cosmological context can only lie in the astrophysical modeling of sources, and neither in the theory nor in the …