Given a compact, connected, oriented 3-manifold $M$ with boundary, and epimorphism $\chi$ from $H_1M$ to a free abelian group $\Pi$, two invariants $\beta$, $\tau \in \bb {Z}\Pi$ are defined. If $M$ embeds in another such 3-manifold $N$ such that $\chi_N$ factors through $\chi$, then the product $\beta\tau$ divides $\Delta_0(H_1\tilde {N})$.A theorem of D. Krebes concerning 4-tangles embedded in links arises as a special case. Algebraic and skein theoretic generalizations for $2n$-tangles provide invariants that persist in the corresponding invariants of links in which they embed. An example is given of a virtual 4-tangle for which Krebesʼs theorem does not hold.