There are the following two notions of "Gauss-Manin connection":

The complex-analytic one: let $f:X\to S$ be a smooth family of complex manifolds. Then we obtain a local system $R^nf_{\ast}\mathbb{C}$ of complex vector spaces on $S$, defining a holomorphic vector bundle $\mathcal{V}=R^nf_{\ast}\mathbb{C}\otimes\mathcal{O}_S$ on $S$ with an integrable connection $\nabla :\mathcal{V}\to\mathcal{V}\otimes\Omega_S^1$. Now the vector bundle $\mathcal{V}$ can be identified with the relative de Rham cohomology $\mathcal{H}_{dR}^n(X/S)$ of the family, so we get a connection on the latter.

The algebraic one: let $f:X\to S$ be a smooth morphism of smooth schemes over a field $k$. Now Katz and Oda in "On the differentiation of De Rham cohomology classes with respect to parameters" (J. Math. Kyoto Univ. 8 (1968), pp. 199-213) construct an integrable connection on $\mathcal{H}_{dR}^n(X/S)$ as some boundary map in a certain spectral sequence.

It is implicit in the literature that these two constructions are compatible, i.e. for a smooth family of smooth varieties over the complex numbers, the connection described in 1. is just the analytification of the one in 2. This sounds pretty reasonable as well. But thinking a bit about it, I was unable to come up with an argument, so could perhaps someone give me a hint where to find this or how to do it?