  While bare diagrammatic series are merely Taylor expansions in powers of
interaction strength, dressed diagrammatic series, built on fully or partially
dressed lines and vertices, are usually constructed by reordering the bare
diagrams, which is an a priori unjustified manipulation, and can even lead to
convergence to an unphysical result [Kozik, Ferrero and Georges, PRL 114,
156402 (2015)]. Here we show that for a broad class of partially dressed
diagrammatic schemes, there exists an action $S^{(\xi)}$ depending analytically
on an auxiliary complex parameter $\xi$, such that the Taylor expansion in
$\xi$ of correlation functions reproduces the original diagrammatic series. The
resulting applicability conditions are similar to the bare case. For fully
dressed skeleton diagrammatics, analyticity of $S^{(\xi)}$ is not granted, and
we formulate a sufficient condition for converging to the correct result.
