  It has been intensively discussed if modifications in the dynamics of the
Universe at late times is able or not to solve the $H_0$ tension. On the other
hand, it has also been argued that the $H_0$ tension is actually a tension on
the supernova absolute magnitude $M_B$. In this work, we robustly constraint
$M_B$ using Pantheon Supernovae Ia (SN) sample, Baryon Acoustic Oscillations
(BAO), and Big Bang Nucleosynthesis (BBN) data, and assess the $M_B$ tension by
comparing three theoretical models, namely the standard $\Lambda$CDM, the
$w$CDM and a non-gravitational interaction (IDE) between dark energy (DE) and
dark matter (DM). We find that the IDE model can solve the $M_B$ tension with a
coupling different from zero at 95\% CL, confirming the results obtained using
a $H_0$ prior.
