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A manufacturing method enabling the obtainment of a functional part essentially formed in a metallic material, all or part of the functional part delimiting a filtering medium permeable to a fluid and delimiting first and second main faces for a preferred circulation of the gas through the filtering medium. The method includes a main phase consisting of an additive manufacturing method in successive passes from a support tray. Each pass includes the deposition of at least one layer of the metallic material, the deposited material adhering to the metallic material deposited before. The deposition is controlled at each pass so the stack of metallic material constitutes the functional part. The filtering medium includes a coalescent network of connecting strands interconnected according to a three-dimensional spatial distribution between the faces, the connecting strands of the network delimiting therebetween pores spatially distributed within the filtering medium in three dimensions between the faces.