  The invariant mass spectra of the $\pi^+\pi^-$ and $\pi^\pm\pi^0$ pairs in
the process $e^+e^- \to \pi^+\pi^-\pi^0$ were studied in the SND experiment at
the VEPP-2M collider in the energy region $\sqrt[]{s} \simeq 1020$ MeV. These
studies were based on about $0.5 \times 10^6$ experimental events. The spectra
were analyzed in the framework of the vector meson dominance model. It was
found that the experimental data can be described with $e^+e^- \to \rho\pi \to
\pi^+\pi^-\pi^0$ transition only. Upper limit on the branching ratio of the
$\phi(1020)\to\pi^+\pi^-\pi^0$ decay through intermediate states different from
$\rho\pi$ was obtained at the 90 % confidence level:
$B(\phi\to\pi^+\pi^-\pi^0)<6 \cdot 10^{-4}$. The $\rho$-meson mass and width
which follow from the spectra analysis are $m_\rho=775.0\pm 1.3$ MeV,
$\Gamma_\rho=150.4 \pm 3.0$ MeV. Neutral and charged $\rho$-mesons mass
difference was found to equal $m_{\rho^\pm}-m_{\rho^0}=-1.3\pm2.3$ MeV. In the
$\pi^+\pi^-$ mass spectrum the $\rho-\omega$ interference was seen at two
standard deviations level.
