We prove that the punctured generalized conifolds and punctured orbifolded
conifolds are mirror symmetric under the SYZ program with quantum corrections.
This mathematically confirms the gauge-theoretic prediction by
Aganagic-Karch-L\"ust-Miemiec, and also provides a supportive evidence to
Morrison's conjecture that geometric transitions are reversed under mirror
symmetry.Comment: v3: one compact example added. 25 pages, 12 figure