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 {\it 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 {\it radio flux} from Vela YZ and Cygnus Loop at all the available frequencies,
the {\it $e^++e^-$ flux} from five experiments from the GeV to tens of TeV energy,
the {\it $e^++e^-$ 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.