  We cross-correlate maps of the thermal Sunyaev-Zeldovich (tSZ) Compton-$y$
parameter published by Planck with the projected distribution of galaxies in a
set of low-redshift tomographic bins. We use the nearly full-sky 2MASS
Photometric Redshift and WISE $\times$ SuperCOSMOS public catalogues, covering
the redshift range $z\lesssim0.4$. Our measurements allow us to place
constraints on the redshift dependence of the mass-observable relation for tSZ
cluster count analyses in terms of the so-called 'hydrostatic mass bias'
parameter $1-b_{\rm H}$. These results can also be interpreted as measurements
of the bias-weighted average gas pressure $\langle bP_e\rangle$ as a function
of redshift, a quantity that can be related to the thermodynamics of gas inside
haloes and used to constrain energy injection processes. We measure $1-b_{\rm
H}$ with $\sim6\%$ precision in 6 equispaced redshift bins, and find no
evidence for a redshift-dependent mass bias parameter, in agreement with
previous analyses. Our mean value of $1-b_{\rm H} = 0.75\pm0.03$ is also in
good agreement with the one estimated by the joint analysis of Planck cluster
counts and CMB anisotropies calibrated with CMB lensing. Our measurements of
$\langle bP_e\rangle$, at the level of $\sim10\%$ in each bin, are the most
stringent constraints on the redshift dependence of this parameter to date, and
agree well both with previous measurements and with theoretical expectations
from shock-heating models.
