Abstract. (Joint with Elizabeth Gasparim) I will describe deformations of the non-compact surfaces Zₖ = Tot (O_{P¹} (–k)) explicitly and discuss their moduli of vector bundles. If time permits, I will also mention how this fits into the framework of deformations of the Abelian category Coh (Zₖ) and further directions involving non-commutative deformations.