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In particular, we give explicit classes for\n  1-parameter Calabi--Yau families.\n  The $q$-hypergeometric origin of our cycles imply\n  that they generate $q$-holonomic modules that define $q$-deformations of the\n  classical Picard-Fuchs equation. 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In particular, we give explicit classes for\n  1-parameter Calabi--Yau families.\n  The $q$-hypergeometric origin of our cycles imply\n  that they generate $q$-holonomic modules that define $q$-deformations of the\n  classical Picard-Fuchs equation. 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