2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101047An open subset U of a complex surface can be topologically perturbed to yield an open subset whose inherited complex structure is Stein, if and only if U is homeomorphic to the interior of a handlebody whose handles all have index equal or less than 2.Comments 23 pages, 5 figures, AMS-LaTeX v2: Overcompressed figures fixed. v3: Minor edits - this is the published versionGeometric TopologyComplex Variables32Q28; 32T05; 57N13text