The invariant mass spectra of the $pi^+pi^-$ and $pi^pmpi^0$ 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 $e^+e^- to rhopi to pi^+pi^-pi^0$ transition only. Upper limit on the branching ratio of the $phi(1020)topi^+pi^-pi^0$ decay through intermediate states different from $rhopi$ was obtained at the 90 % confidence level: $B(phitopi^+pi^-pi^0)<6 cdot 10^{-4}$. The $rho$-meson mass and width which follow from the spectra analysis are $m_rho=775.0pm 1.3$ MeV, $Gamma_rho=150.4 pm 3.0$ MeV. Neutral and charged $rho$-mesons mass difference was found to equal $m_{rho^pm}-m_{rho^0}=-1.3pm2.3$ MeV. In the $pi^+pi^-$ mass spectrum the $rho-omega$ interference was seen at two standard deviations level.
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