  Comparing the parameterized post-Newtonian parameter $\gamma$ values for
different types of particles, or the same type of particles with different
energies is an important method to test the Einstein Equivalence Principle
(EEP). Assuming that the observed time delays are dominated by the
gravitational potential of the Laniakea supercluster of galaxies, better
results of EEP constraints can be obtained. In this paper, we apply photons
from three kinds of cosmic transients, including TeV blazars, gamma-ray bursts
as well as fast radio bursts to constrain EEP. With a gravitational field far
more stronger than a single galaxy, we obtain 4--5 orders of magnitude more
stringent than the pervious results.
