I will present a result which is an equivalence of categories between meromorphic sl(2)-connections with prescribed residues and abelian meromorphic connections. I will describe the construction of the functor and explain why it is an equivalence by building an explicit inverse functor. The importance of this equivalence is that the moduli spaces corresponding to these categories are known to be holomorphic symplectic, and this equivalence descends to a local symplectomorphism. The moduli space of abelian connections involved in the correspondence is a torsor for an algebraic torus, so this local symplectomorphism is in fact a holomorphic Darboux coordinate system on the moduli space of sl(2)-connections, as was described in the work on Spectral Networks by Gaiotto-Moore-Neitzke.