  Within the block spin renormalization group we are able to construct the
"exact" phase diagram of the XYZ spin chain. First we identify the Ising order
along $\hat x$ or $\hat y$ as attractive renormalization group fixed points of
the Kitaev chain. Then in a global phase space composed of the anisotropy
$\lambda$ of the XY interaction and the coupling $\Delta$ of the
$\Delta\sigma^z\sigma^z$ interaction we find that the above fixed points remain
attractive in the two dimesional parameter space. We therefore classify the
gapped phases of the XYZ spin chain as: (1) either attracted to the Ising limit
of the Kitaev-chain which in turn is characterized by winding number $\pm 1$
depending whether the Ising order parameter is along $\hat x$ or $\hat y$
directions; or (2) attracted to the Mott phases of the underlying Jordan-Wigner
fermions which is characterized by zero winding number. We therefore establish
that the exact phase boundaries of the XYZ model in Baxter's solution indeed
correspond to topological phase transitions. The topological nature of the
phase transitions of the XYZ model justifies why our analytical solution of the
three-site problem which is at the core of the renormalization group treatment
is able to produce the exact phase diagram of Baxter's solution. We argue that
the distribution of the winding numbers between the three Ising phases is a
matter of choice of the coordinate system, and therefore the Mott-Ising phase
is entitled to host apprpriate form of zero modes. We further observe that the
renormalization group flow can be cast into a geometric progression of a
properly identified parameter. We show that this new parameter is actually the
size of the (Majorana) zero modes.
