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).