  Let $\pi\colon\mathscr{X}\rightarrow\mathscr{Y}$ be an extension of minimal
compact metric flows such that $\texttt{R}_\pi\not=\Delta_X$. A subflow of
$\texttt{R}_\pi$ is called an M-flow if it is T.T. and contains a dense set of
a.p. points. In this paper we mainly prove the following:
  (1) $\pi$ is PI iff $\Delta_X$ is the unique M-flow containing $\Delta_X$ in
$\texttt{R}_\pi$.
  (2) If $\pi$ is not PI, then there exists a canonical Li-Yorke chaotic M-flow
in $\texttt{R}_\pi$. In particular, an Ellis weak-mixing non-proximal extension
is non-PI and so Li-Yorke chaotic.
  (3) A unbounded or non-minimal M-flow, not necessarily compact, is sensitive
on initial conditions.
  (4) every syndetically distal flow is pointwise Bohr a.p.
