Cellular biology abound with filaments interacting through fluids, from intracellular microtubules, to rotating flagella and beating cilia. While previous work has demonstrated the complexity of capturing nonlocal hydrodynamic interactions between moving filaments, the problem remains difficult theoretically. We show here that when filaments are closer to each other than their relevant length scale, the integration of hydrodynamic interactions can be approximately carried out analytically. This leads to a set of simplified local equations, illustrated on a simple model of two interacting filaments, which can be used to tackle theoretically a range of problems in biology and physics.