Exotic codimension-1 submanifolds in 4-manifolds and stabilizations

In a small simply-connected closed 4-manifold, we construct infinitely many pairs of exotic codimension-$1$ submanifolds with diffeomorphic complements that remain exotic after any number of stabilizations by $S^2\times S^2$. We also give new constructions of exotic embeddings of 3-spheres in 4-manifolds with diffeomorphic complements.