In this paper, we characterize surgery presentations for $mathbb{Z}$-homology 3-spheres and $mathbb{Z}/2mathbb{Z}$-homology 3-spheres obtained from $S^3$ by Dehn surgery along a knot or link which admits an even net diagram and show that the Casson invariant for $mathbb{Z}$-homology spheres and the ${mu}$-invariant for $mathbb{Z}/2mathbb{Z}$-homology spheres can be directly read from the net diagram. We also construct oriented 4-manifolds bounding such homology spheres and find their some properties.