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Let $\pi_1:\mathcal{X} \to \Delta$ be a flat family of smooth, projectivecurves of genus $g \ge 2$, degenerating to an irreducible nodal curve $X_0$with exactly one node. Fix an invertible sheaf $\mathcal{L}$ on $\mathcal{X}$of relative odd degree. Let $\pi_2:\mathcal{G}(2,\mathcal{L}) \to \Delta$ bethe relative Gieseker moduli space of rank $2$ semi-stable vector bundles withdeterminant $\mathcal{L}$ over $\mathcal{X}$. Since $\pi_2$ is smooth over$\Delta^*$, there exists a canonical family$\widetilde{\rho}_i:\mathbf{J}^i_{\mathcal{G}(2, \mathcal{L})_{\Delta^*}} \to\Delta^{*}$ of $i$-th intermediate Jacobians i.e., for all $t \in \Delta^*$,$(\widetilde{\rho}_i)^{-1}(t)$ is the $i$-th intermediate Jacobian of$\pi_2^{-1}(t)$. There exist different N\'{e}ron models$\overline{\rho}_i:\overline{\mathbf{J}}_{\mathcal{G}(2, \mathcal{L})}^i \to\Delta$ extending $\widetilde{\rho}_i$ to the entire disc $\Delta$, constructedby Clemens, Saito, Schnell, Zucker and Green-Griffiths-Kerr. In this article,we prove that in our setup, the N\'{e}ron model $\overline{\rho}_i$ iscanonical in the sense that the different N\'{e}ron models coincide and is ananalytic fiber space which graphs admissible normal functions. We also showthat for $1 \le i \le \max\{2,g-1\}$, the central fiber of $\overline{\rho}_i$is a fibration over product of copies of $J^k(\mathrm{Jac}(\widetilde{X}_0))$for certain values of $k$, where $\widetilde{X}_0$ is the normalization of$X_0$. In particular, for $g \ge 5$ and $i=2, 3, 4$, the central fiber of$\overline{\rho}_i$ is a semi-abelian variety. Furthermore, we prove that the$i$-th generalized intermediate Jacobian of the (singular) central fibre of$\pi_2$ is a fibration over the central fibre of the N\'{e}ron model$\overline{\mathbf{J}}^i_{\mathcal{G}(2, \mathcal{L})}$. In fact, for $i=2$ thefibration is an isomorphism.

N\'{e}ron models of intermediate Jacobians associated to moduli spaces