  The goal of this paper is to provide a new analysis of the classical dynamics
of Bianchi type I, II and IX models by applying conventional Hamiltonian
methods in the language of Ashtekhar variables. We show that Bianchi type II
models can be seen as a perturbation of Bianchi I ones, and integrated. Bianchi
IX models can be seen, in turn, as a perturbation of Bianchi IIs, but here the
integration algorithm breaks down. This is an ''interesting failure'', bringing
light onto the chaotic nature of Bianchi type IX dynamics.As a by product of
our analysis we filled some gaps in the literature, such us recovering the BKL
map in this context.
