  The data on the inclusive flux of cosmic positrons and electrons
($e^++e^{-}$) have been recently collected from GeV to tens of TeV energies by
several experiments with unprecedented precision. In addition, the Fermi-LAT
Collaboration has provided a new energy spectrum for the upper bounds on the
$e^++e^{-}$ dipole anisotropy. This observable can bring information on the
emission from local Galactic sources, notably measured with high precision at
radio frequencies. We develop a framework in which $e^-$ and $e^+$ measured at
Earth from GeV up to tens of TeV energies have a composite origin. A dedicated
analysis is deserved to Vela YZ and Cygnus Loop Supernova Remnants (SNRs), for
which we consider two different models for the injection of $e^-$. We
investigate the consistency of these models using the three physical
observables: the radio flux from Vela YZ and Cygnus Loop at all the available
frequencies, the $e^++e^-$ flux from five experiments from the GeV to tens of
TeV energy, the $e^++e^-$ dipole anisotropy upper limits from 50 GeV to about 1
TeV. We find that the radio flux for these nearby SNRs strongly constraints the
properties of the injection electron spectrum, partially compatible with the
looser constraints derived from the $e^+ + e^-$ flux data. We also perform a
multi-wavelength multi-messenger analysis by fitting simultaneously the radio
flux on Vela YZ and Cygnus Loop and the $e^+ + e^-$ flux, and checking the
outputs against the $e^+ + e^-$ dipole anisotropy data. Remarkably, we find a
model which is compatible with all the $e^++e^-$ flux data, the radio data for
Vela YZ and Cygnus Loop, and with the anisotropy upper bounds. We show the
severe constraints imposed by the most recent data on the $e^+ + e^-$ dipole
anisotropy.
