the KPZ non-linear term could be reabsorbed using $n=\exp(-\alpha h)$ with a proper choice of $\alpha$). This transformation maps the depinning from the wall $\langle h \rangle \to \infty$ to a transition into an absorbing state $\n \to 0$. The physical equivalence between the cases $\lambda>0$ with a lower-wall ($p>0$), and $\lambda<0$ with an upper wall ($p<0$), reflects in the fact that the same equation is obtained using $n=\exp(-h)$ and $n=\exp h$, respectively.

Observe that Eq.(\[mnminus\]) is identical to the MN equation describing the MN1 class [@MN1; @MN2; @Review], except for the presence of an extra term $ (\nabla n)^2 /n $. This term can also be written as $(\nabla n) \cdot (\nabla \ln(n)) = (\nabla n ) \cdot (\nabla h)$ suggesting that the interface language is the natural one for this class. In fact, except for the factor 2 in front of $(\nabla n)^2 /n$ Eq. (\[mnminus\]) coincides with the Cole-Hopf transform of $$\partial_t h (x,t) = \nabla^2 h + a +b e^{-ph} + \eta(x,t)$$ that describes the growth of wetting layers toward their equilibrium state [@lipowsky] (observe that this is just the equilibrium, Edwards-Wilkinson model, in the presence of a bounding wall). Note also that the factor $2$ 