Genomic rearrangements and associated copy number changes are important drivers in cancer as they can alter the expression of oncogenes and tumor suppressors, create gene fusions, and misregulate gene expression. Here we present SplitThreader (http://splitthreader.com), an open- source interactive web application for analysis and visualization of genomic rearrangements and copy number variation in cancer genomes. SplitThreader constructs a sequence graph of genomic rearrangements in the sample and uses a priority queue breadth-first search algorithm on the graph to search for novel interactions. This is applied to detect gene fusions and other novel sequences, as well as to evaluate distances in the rearranged genome between any genomic regions of interest, especially the repositioning of regulatory elements and their target genes. SplitThreader also analyzes each variant to categorize it by its relation to other variants and by its copy number concordance. This identifies balanced translocations, identifies simple and complex variants, and suggests likely false positives when copy number is not concordant across a candidate breakpoint. It also provides explanations when multiple variants affect the copy number state and obscure the contribution of a single variant, such as a deletion within a region that is overall amplified. Together, these categories triage the variants into groups and provide a starting point for further systematic analysis and manual curation. To demonstrate its utility, we apply SplitThreader to three cancer cell lines, MCF-7 and A549 with Illumina paired- end sequencing, and SK-BR-3, with long-read PacBio sequencing. Using SplitThreader, we examine the genomic rearrangements responsible for previously observed gene fusions in SK-BR-3 and MCF-7, and discover many of the fusions involved a complex series of multiple genomic rearrangements. We also find notable differences in the types of variants between the three cell lines, in particular a much higher proportion of reciprocal variants in SK-BR-3 and a distinct clustering of interchromosomal variants in SK-BR-3 and MCF-7 that is absent in A549.