Time series exploration and mining has many applications across several industrial and scientific domains. In this paper, we consider the problem of detecting locally similar pairs and groups, called bundles, over co-evolving time series. These are pairs or groups of subsequences whose values do not differ by more than ε for at least delta consecutive timestamps, thus indicating common local patterns and trends. We first present a baseline algorithm that performs a sweep line scan across all timestamps to identify matches. Then, we propose a filter-verification technique that only examines candidate matches at judiciously chosen checkpoints across time. Specifically, we introduce two block scanning algorithms for discovering local pairs and bundles respectively, which leverage the potential of checkpoints to aggressively prune the search space. We experimentally evaluate our methods against real-world and synthetic datasets, demonstrating a speed-up in execution time by an order of magnitude over the baseline. This paper has been published in the 16th International Symposium on Spatial and Temporal Databases (SSTD19).