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We study infinite-distance limits in the complex structure moduli space ofelliptic Calabi-Yau threefolds. In F-theory compactifications to sixdimensions, such limits include infinite-distance trajectories in thenon-perturbative open string moduli space. The limits are described asdegenerations of elliptic threefolds whose central elements exhibit non-minimalelliptic fibers, in the Kodaira sense, over curves on the base. We show howthese non-crepant singularities can be removed by a systematic sequence ofblow-ups of the base, leading to a union of log Calabi-Yau spaces gluedtogether along their boundaries. We identify criteria for the blow-ups to giverise to open chains or more complicated trees of components and analyse theblow-up geometry. While our results are general and applicable to allnon-minimal degenerations of Calabi-Yau threefolds in codimension one, weexemplify them in particular for elliptic threefolds over Hirzebruch surfacebase spaces. We also explain how to extract the gauge algebra for F-theoryprobing such reducible asymptotic geometries. This analysis is the basis for adetailed F-theory interpretation of the associated infinite-distance limitsthat will be provided in a companion paper.

Non-minimal Elliptic Threefolds at Infinite Distance I: Log Calabi-Yau Resolutions