  We provide the first combined cosmological analysis of South Pole Telescope
(SPT) and Planck cluster catalogs. The aim is to provide an independent
calibration for Planck scaling relations, exploiting the cosmological
constraining power of the SPT-SZ cluster catalog and its dedicated weak lensing
(WL) and X-ray follow-up observations. We build a new version of the Planck
cluster likelihood. In the $\nu \Lambda$CDM scenario, focusing on the mass
slope and mass bias of Planck scaling relations, we find $\alpha_{\text{SZ}} =
1.49_{-0.10}^{+0.07}$ and $(1-b)_{\text{SZ}} = 0.69_{-0.14}^{+0.07}$
respectively. The results for the mass slope show a $\sim 4 \, \sigma$
departure from the self-similar evolution, $\alpha_{\text{SZ}} \sim 1.8$. This
shift is mainly driven by the matter density value preferred by SPT data,
$\Omega_m = 0.30 \pm 0.03$, lower than the one obtained by Planck data alone,
$\Omega_m = 0.37_{-0.06}^{+0.02}$. The mass bias constraints are consistent
both with outcomes of hydrodynamical simulations and external WL calibrations,
$(1-b) \sim 0.8$, and with results required by the Planck cosmic microwave
background cosmology, $(1-b) \sim 0.6$. From this analysis, we obtain a new
catalog of Planck cluster masses $M_{500}$. We estimate the ratio between the
published Planck $M_{\text{SZ}}$ masses and our derived masses $M_{500}$, as a
"measured mass bias", $(1-b)_M$. We analyse the mass, redshift and detection
noise dependence of $(1-b)_M$, finding an increasing trend towards high
redshift and low mass. These results mimic the effect of departure from
self-similarity in cluster evolution, showing different dependencies for the
low-mass high-mass, low-z high-z regimes.
