Degenerating algebraic varieties has been an important tool to study birational geometry in the past 10 years. There are many ways to understand the geometric fiber of a degeneration using the special fiber: e.g. (1) the dual complex, (2) the decomposition of the diagonal, and (3) the motivic volume. In this talk we introduce a chain complex that we attach to such a degeneration that is (A) functorial, and (B) a stable birational invariant of the geometric fiber. This invariant lives somewhere between (1), (2), and (3). As an application, we show that A1-connectedness specializes in smooth projective families. This is joint work with James Hotchkiss.