  We discuss the theory of Coleman families interpolating critical-slope
Eisenstein series. We apply it to study degeneration phenomena at the level of
Euler systems. In particular, this allows us to prove relations between Kato
elements, Beilinson--Flach classes and diagonal cycles, and also between
Heegner cycles and elliptic units. We expect that this method could be extended
to construct new instances of Euler systems.
