Why can Kontsevich's invariants detect exotic phenomena?

In topology, the difference between the category of smooth manifolds and the category of topological manifolds has always been a delicate and intriguing problem, called the "exotic phenomena". The recent work of Watanabe (2018) uses the tool "Kontsevich's invariants" to show that the group of diffeomorphisms of the 4-dimensional ball, as a topological group, has non-trivial homotopy type. In contrast, the group of homeomorphisms of the 4-dimensional ball is contractible. Kontsevich's invariants, defined by Kontsevich in the early 1990s from perturbative Chern-Simons theory, are invariants of (certain) 3-manifolds / fiber bundles / knots and links (it is the same argument in different settings). Watanabe's work implies that these invariants detect exotic phenomena, and, since then, they have become an important tool in studying the topology of diffeomorphism groups. It is thus natural to ask: how to understand the role smooth structure plays in Kontsevich's invariants? My recent work provides a perspective on this question: the real blow-up operations on a smooth manifold depend on the smooth structure in an essential way; thus, the topology of the spaces obtained by doing some blow-ups on a smooth manifold/fiber bundle X encodes information of the smooth structure on X.