  In this paper we show that the non-alternating torus knots are homologically
thick, i.e. that their Khovanov homology occupies at least three diagonals.
Furthermore, we show that we can reduce the number of full twists of the torus
knot without changing certain part of its homology, and consequently, we show
that there exists stable homology of torus knots conjectured by Dunfield, Gukov
and Rasmussen in \cite{dgr}. Since our main tool is the long exact sequence in
homology, we have applied our approach in the case of the Khovanov-Rozansky
($sl(n)$) homology, and thus obtained analogous stability properties of $sl(n)$
homology of torus knots, also conjectured in \cite{dgr}.
