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Mateo Maza is the son of Manuel Maza and Baldamera Lastra Gomez. His siblings were Jose Maza, Gabino Maza, Luis Maza, Antonia Maza, Isidro Maza, Maria Maza, Baldomera Maza, Manuel Maza, Alfredo Maza I, Alfredo Maza II, Esperanza Maza.
Mateo Maza's wife is Martina Diaz.