Mining condensed representations of frequent itemsets (FI), namely frequent closures (FCIs) or generators (FGIs), over a stream is already a challenging task, and mining both is even more so. Yet, FGIs and FCIs jointly serve in many practical settings and underlie popular association rule bases. To date, the only way to approach the task is by the (impractical) combination of two dedicated miners. As a remedy, we propose a novel joint miner implementing a holistic approach –emphasizing the underlying equivalence classes– to the joint maintenance of FGIs and FCIs upon stream updates. With a sliding window mining schema, we build upon known results on window expansion and provide novel results on window shrinking while adapting both to the support-based filtering. Thus, through the collaborative maintenance of both FCI and FGI, our method achieves effort factoring that helps it outperform its sole FGI stream mining competitor and keep up with two FCI ones.