  We analyze the role of final state interactions in decay of the lighest
exotic meson, $pi_1$ with $J^{PC}=1^{-+}. We use the relativistic
Lippmann-Schwinger equation for two coupled $\pi b_{1}$ and $\pi\rho$ channels.
The first one is the predicted dominant decay mode of the $\pi_{1}$, whereas in
the other a narrow $\pi_1(1600)$ exotic signal has been reported by the E852
collaboration. The FSI potential is constructed, based on the $\omega$ meson
exchange between the two channels. We find that this process introduces
corrections to the $\pi_{1}$ widths of the order of only a few MeV. Therefore,
we conclude that a substantial $\pi\rho$ mode cannot be generated through level
mixing.
