  We demonstrate that Feynman integrals of a fixed diagram form a flat vector
bundle over the complement of Landau varieties that possesses a connection
\begin{equation} \frac{\partial}{\partial
p_{i,\mu}}f_\beta(p_{i,\mu})=\sum_{\beta'} \sum_k \sum_{I_1,...,I_k}
\frac{A^{I_1,...,I_k}_{i,\mu,\beta,\beta'}(p)}{L_{I_1}(p)...L_{I_k}(p)}
f_{\beta'}(p) \end{equation} where $L_I(p)$ are the Landau polynomials
(multidiscriminants). This is the Gauss-Manin connection for the original
integral. This result suggests a shift of focus from the integrals to the
geometry of the complement of Landau varieties and Riemann-Hilbert data
associated with these varieties.
