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We reanalyze the recently released SH0ES data for the determination of $H_0$.We focus on testing the homogeneity of the Cepheid+SnIa sample and therobustness of the results in the presence of new degrees of freedom in themodeling of Cepheids and SnIa. We thus focus on the four modeling parameters ofthe analysis: the fiducial luminosity of SnIa $M_B$ and Cepheids $M_W$ and thetwo parameters ($b_W$ and $Z_W$) standardizing Cepheid luminosities with periodand metallicity. After reproducing the SH0ES baseline model results, we allowfor a transition of the value of any one of these parameters at a givendistance $D_c$ or cosmic time $t_c$ thus adding a single degree of freedom inthe analysis. When the SnIa absolute magnitude $M_B$ is allowed to have atransition at $D_c\simeq 50Mpc$ (about $160Myrs$ ago), the best fit value ofthe Hubble parameter drops from $H_{0}=73.04\pm1.04\,km\,s^{-1}\,Mpc^{-1}$ to$H_0=67.32\pm 4.64\, km\,s^{-1}\,Mpc^{-1}$ in full consistency with the Planckvalue. Also, the best fit SnIa absolute magnitude $M_B^>$ for $D>D_c$ drops tothe Planck inverse distance ladder value $M_{B}^>=-19.43\pm 0.15$ while the lowdistance best fit $M_B^<$ parameter remains close to the original distanceladder calibrated value $M_{B}^<=-19.25\pm 0.03$. Similar hints for atransition behavior is found for the other three main parameters of theanalysis ($b_W$, $M_W$ and $Z_W$) at the same critical distance $D_c\simeq50\,Mpc$ even though in that case the best fit value of $H_0$ is notsignificantly affected. When the inverse distance ladder constraint on $M_B^>$is included in the analysis, the uncertainties for $H_0$ reduce dramatically($H_0= 68.2\pm 0.8\, km\,s^{-1}\,Mpc^{-1}$) and the $M_B$ transition model isstrongly preferred over the baseline SH0ES model ($\Delta \chi^2 \simeq -15$,$\Delta AIC \simeq -13$) according to AIC and BIC model selection criteria.

A reanalysis of the latest SH0ES data for $H_0$: Effects of new degrees of freedom on the Hubble tension