A turbomachine, comprising: a plurality of transition ducts disposed in a generally annular array and comprising a first transition duct and a second transition duct, each of the plurality of transition ducts comprising an inlet, an outlet, and a passage defining an interior and extending between the inlet and the outlet and defining a longitudinal axis, a radial axis, and a tangential axis, the outlet of each of the plurality of transition ducts offset from the inlet along the longitudinal axis and the tangential axis, the outlet of at least one transition duct of the plurality of transition ducts comprising an inner flange and an outer flange; a support ring assembly downstream of the plurality of transition ducts along a hot gas path; a plurality of bore holes defined in the inner flange and outer flange; a plurality of mating bore holes (181, 183) defined in the support ring assembly; and a plurality of mechanical fasteners connecting the inner flange and the outer flange of the at least one transition duct to the support ring assembly, each of the plurality of mechanical fasteners extending through a bore hole and mating bore hole (181, 183), characterized in that: wherein a first one of the bore holes or mating bore holes (181, 183) has a first maximum radial gap and a first maximum tangential gap relative to the mechanical fastener extending through the first one of the bore holes or mating bore holes (181, 183), wherein a second one of the bore holes or mating bore holes (181, 183) has a second maximum radial gap and a second maximum tangential gap relative to the mechanical fastener extending through the second one of the bore holes or mating bore holes (181, 183), and wherein the second maximum radial gap is greater than the first maximum radial gap or the second maximum tangential gap is greater than the first maximum tangential gap. a plurality of transition ducts disposed in a generally annular array and comprising a first transition duct and a second transition duct, each of the plurality of transition ducts comprising an inlet, an outlet, and a passage defining an interior and extending between the inlet and the outlet and defining a longitudinal axis, a radial axis, and a tangential axis, the outlet of each of the plurality of transition ducts offset from the inlet along the longitudinal axis and the tangential axis, the outlet of at least one transition duct of the plurality of transition ducts comprising an inner flange and an outer flange; a support ring assembly downstream of the plurality of transition ducts along a hot gas path; a plurality of bore holes defined in the inner flange and outer flange; a plurality of mating bore holes (181, 183) defined in the support ring assembly; and a plurality of mechanical fasteners connecting the inner flange and the outer flange of the at least one transition duct to the support ring assembly, each of the plurality of mechanical fasteners extending through a bore hole and mating bore hole (181, 183), characterized in that: wherein a first one of the bore holes or mating bore holes (181, 183) has a first maximum radial gap and a first maximum tangential gap relative to the mechanical fastener extending through the first one of the bore holes or mating bore holes (181, 183), wherein a second one of the bore holes or mating bore holes (181, 183) has a second maximum radial gap and a second maximum tangential gap relative to the mechanical fastener extending through the second one of the bore holes or mating bore holes (181, 183), and wherein the second maximum radial gap is greater than the first maximum radial gap or the second maximum tangential gap is greater than the first maximum tangential gap. wherein a first one of the bore holes or mating bore holes (181, 183) has a first maximum radial gap and a first maximum tangential gap relative to the mechanical fastener extending through the first one of the bore holes or mating bore holes (181, 183), wherein a second one of the bore holes or mating bore holes (181, 183) has a second maximum radial gap and a second maximum tangential gap relative to the mechanical fastener extending through the second one of the bore holes or mating bore holes (181, 183), and wherein the second maximum radial gap is greater than the first maximum radial gap or the second maximum tangential gap is greater than the first maximum tangential gap.