Eisenstein congruences among Euler systems

We investigate Eisenstein congruences between the so-called Euler systems of Garrett--Rankin--Selberg type. This includes the cohomology classes of Beilinson--Kato, Beilinson--Flach and diagonal cycles. The proofs crucially rely on different known versions of the Bloch--Kato conjecture, and are based on the study of the Perrin-Riou formalism and the comparison between the different $p$-adic $L$-functions.