We prove that the moduli space of holonomy $G_{2}$ -metrics on a closed 7-manifold can be disconnected by presenting a number of explicit examples. We detect different connected components of the $G_{2}$ -moduli space by defining an analytic refinement $\bar{\nu }(M, g) \in \mathbb{Z}$ of the defect invariant $\nu (M,\varphi )\in \mathbb{Z}/48$ of $G_{2}$ -structures $\varphi $ on a closed 7-manifold $M$ introduced by the first and third authors. The $\bar{\nu }$ -invariant is defined using $\eta $ -invariants and Mathai-Quillen currents on $M$ and we compute it for twisted connected sums à la Kovalev, Corti-Haskins-Nordström-Pacini and extra-twisted connected sums as constructed by the second and third authors. In particular, we find examples of $G_{2}$ -holonomy metrics in different components of the moduli space where the associated $G_{2}$ -structures are homotopic and other examples where they are not.
