There is a strong discrepancy between the value of the Hubble parameter $$H_0^P$$ H 0 P obtained from large scale observations such as the Planck mission, and the small scale value $$H_0^R$$ H 0 R , obtained from low redshift supernovae (SNe). The value of the absolute magnitude $$M^{Hom}$$ M Hom used as prior in analyzing observational data is obtained from low-redshift SNe, assuming a homogeneous Universe, but the distance of the anchors used to calibrate the SNe to obtain M would be affected by a local inhomogeneity, making it inconsistent to test the Copernican principle using $$M^{Hom}$$ M Hom , since M estimation itself is affected by local inhomogeneities. We perform an analysis of the luminosity distance of low redshift SNe, using different values of M, $$\{M^P,M^R\}$$ { M P , M R } , corresponding to different values of $$H_0$$ H 0 , $$\{H_0^P,H_0^R\}$$ { H 0 P , H 0 R } , obtained from the model independent consistency relation between $$H_0$$ H 0 and M which can be derived from the definition of the distance modulus. We find that the value of M can strongly affect the evidence of a local inhomogeneity. We analyze data from the Pantheon catalog, finding no significant statistical evidence of a local inhomogeneity using the parameters $$\{M^R,H_0^R\}$$ { M R , H 0 R } , confirming previous studies, while with $$\{M^P,H_0^P\}$$ { M P , H 0 P } we find evidence of a small local void, which causes an overestimation of $$M^R$$ M R with respect to $$M^P$$ M P . An inhomogeneous model with the parameters $$\{M^P,H_0^P\}$$ { M P , H 0 P } fits the data better than a homogeneous model with $$\{M^R,H_0^R\}$$ { M R , H 0 R } , resolving the apparent $$H_0$$ H 0 tension. Using $$\{M^P,H_0^P\}$$ { M P , H 0 P } , we obtain evidence of a local inhomogeneity with a density contrast $$-0.140 \pm 0.042 $$ - 0.140 ± 0.042 , extending up to a redshift of $$z_v =0.056 \pm 0.0002$$ z v = 0.056 ± 0.0002 , in good agreement with recent results of galaxy catalogs analysis (Wong et al. in The local hole: a galaxy under-density covering 90 mpc, 2021).

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