  We define a diagram associated to any algebraic connection on a vector bundle
on a Zariski open subset of the Riemann sphere, extending the definition of
Boalch-Yamakawa to the general case featuring several irregular singularities,
possibly ramified. We prove that the diagram is invariant under the symplectic
automorphisms of the Weyl algebra, encompassing the Fourier-Laplace transform.
As an application, we establish several new cases of the observation that
different Lax representations of a given Painlev\'e-type equation may be read
off directly from the diagram, corresponding to connections with different
formal data, usually on different rank bundles.
