I will present a work in progress that I am developping jointly with S. Ciani and I. Skrypnik, about the degenerate parabolic equation of Trudinger type in anisotropic form. After recalling the fundamental solutions of Barenblatt type in the anisotropic regime, and the associated sub-potential estimates, I will present a weak Harnack inequality that is adapted to the intrinsic geometry of the problem, and via this inequality I will prove some rigidity results for the non-negative solutions of the equation. This approach opens to a possible extension of the De Giorgi-Nash-Moser theory in non-isotropic setting.