  We present an analytical modelling of the angular cross-correlations between
the Integrated Sachs Wolfe-Rees Sciama (ISWRS) effect and large-scale structure
tracers in the presence of massive neutrinos. Our method has been validated
against large N-body simulations with a massive neutrino particle component,
namely the DEMNUni suite. We investigate the impact of different neutrino
masses on the cross-correlations between the ISWRS effect and both the galaxy
clustering and the lensing of the Cosmic Microwave Background (CMB). We also
test the ability of current nonlinear matter power spectrum modellings to
reproduce neutrino effects in such cross-correlations. We show that the
multipole position of a characteristic sign inversion in the cross-spectra, due
to nonlinear effects, is strongly related to the total neutrino mass $M_\nu$
and depends almost linearly on it. While these nonlinear cross-correlation
signals may not be able alone to constrain the neutrino mass, our approach
paves the way to the detection of such cross-spectra on small scales for their
exploitation in combination with main probes from future galaxy surveys and CMB
experiments.
