  We propose that the unified Fano-like interference picture applies to
$e^+e^-\to \pi^+\pi^- J/\psi$ and $e^+e^-\to \pi^+\pi^- \psi(3686)$, where
$Y(4260)$ and $Y(4360)$ are observed, respectively, to provide a reasonable
interpretation of the asymmetric lines hapes of $Y(4260)$ and $Y(4360)$
structures. Moreover, the Fano-like interference induces an extra broad
structure $Y(4008)$ in $e^+e^-\to \pi^+\pi^- J/\psi$ as a companion peak to
$Y(4260)$. Three charmonium-like states $Y(4008)$, $Y(4260)$ and $Y(4360)$
observed in $e^+e^-$ annihilation processes are not genuine resonances. Under
this scenario, it is well explained why $Y(4008)$, $Y(4260)$ and $Y(4360)$ are
absent in the experimental data of the $R$ value scan and missing in open-charm
decay channels. Although the present work presents a typical application of the
Fano-like interference in particle physics at the lower energy region, we have
reason to believe that the Fano-like phenomena may exist in other processes
such as $e^+e^-\to \pi^+\pi^-\psi(3770)$ and $e^+e^-\to K^+K^- J/\psi$, which
will be accessible at BESIII and forthcoming BelleII.
