  Let $p$ be an odd prime. Let $f_1$ and $f_2$ be weight-two Hecke
eigen-cuspforms with isomorphic residual Galois representations at $p$.
Greenberg--Vatsal and Emerton--Pollack--Weston showed that if $p$ is a good
ordinary prime for the two forms, the Iwasawa invariants of their $p$-primary
Selmer groups and $p$-adic $L$-functions over the cyclotomic
$\mathbb{Z}_p$-extension of $\mathbb{Q}$ are closely related. The goal of this
article is to generalize these results to the anticyclotomic setting. More
precisely, let $K$ be an imaginary quadratic field where $p$ splits. Suppose
that the generalized Heegner hypothesis holds with respect to both $(f_1,K)$
and $(f_2,K)$. We study relations between the Iwasawa invariants of the BDP
Selmer groups and the BDP $p$-adic $L$-functions of $f_1$ and $f_2$.
