  Motivated by the Atiyah-Floer conjecture, we consider $SO(3)$ Santi-self-dual
instantons on the product of the real line and a three-manifold with
cylindrical end. We prove a Gromov-Uhlenbeck type compactness theorem, namely,
any sequence of such instantons with uniform energy bound has a subsequence
converging to a type of singular objects which may have both instanton and
holomorphic curve components. This result is the first step towards
constructing a natural bounding cochain proposed by Fukaya for the $SO(3)$
Atiyah-Floer conjecture.
