This position paper presents the trend of the research focus transition from mobility management to connectivity management, for the emerging pervasive and ubiquitous computing paradigm. Traditional perspective on mobility and QoS resource management is summarized. Scenarios of heterogeneous multi-access networks are introduced, and new requirements are analysed. Three main tasks of connectivity management are presented. First connectivity is defined as one source of context beyond networking resource. Second features and benefits of flow level vertical handoff are discussed comparing to device level handoff scheme. Third the potential application based on the new conception of connectivity collaboration is presented. A connectivity management framework is outlined in containing the defined functionalities.