We describe deformations of noncompact Calabi-Yau threefoldsWk := Tot(OP1 (-k) ⊕ OP1 (k - 2)),for k = 1, 2, 3. We compute deformations concretely by calculations of the cohomology group H1(Wk, TWk) via Čech cohomology. We show that for each k = 1, 2, 3 the associated structures are qualitatively different, and we also comment on their differences from the analogous structures of simpler non-compact twofolds Tot(OP1 (-k)).Describimos deformaciones de 3-variedades Calabi-Yau no compactasWk := Tot(OP1 (-k) ⊕ OP1 (k - 2)),para k = 1, 2, 3. Concretamente, calculamos las deformaciones a través del primer grupo de cohomología H1(Wk, TWk) vía cohomología de Čech. Mostramos que para cada k = 1, 2, 3 las estructuras asociadas son cualitativamente distintas y, además, comentamos sobre sus diferencias con las estructuras análogas de las 2-variedades no compactas Tot(OP1 (-k)).