Geospatial data constitutes a considerable part of (Semantic) Web data, but so far, its sources are inadequately interlinked in the Linked Open Data cloud. Geospatial Interlinking aims to cover this gap by associating geometries with topological relations like those of the Dimensionally Extended 9-Intersection Model. Due to its quadratic time complexity, various algorithms aim to carry out Geospatial Interlinking efficiently. We present JedAI-spatial, a novel, open-source system that organizes these algorithms according to three dimensions: (i) Space Tiling, which determines the approach that reduces the search space, (ii) Budget-awareness, which distinguishes interlinking algorithms into batch and progressive ones, and (iii) Execution mode, which discerns between serial algorithms, running on a single CPU-core, and parallel ones, running on top of Apache Spark. We analytically describe JedAI-spatial's architecture and capabilities and perform thorough experiments to provide interesting insights about the relative performance of its algorithms.