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We propose the intermittently tethered unmanned aerial vehicle (iTUAV) as a tradeoff between the power availability of a tethered UAV (TUAV) and the flexibility of an untethered UAV. An iTUAV can provide cellular connectivity while being temporarily tethered to the most adequate ground anchor. Also, it can flexibly detach from one anchor, travel, then attach to another one to maintain/improve the coverage quality for mobile users. Hence, we discuss here the existing UAV-based cellular networking technologies, followed by a detailed description of the iTUAV system, its components, and mode of operation. Subsequently, we present a comparative study of the existing and proposed systems highlighting the differences in key features such as mobility and energy. To emphasize the potential of iTUAV systems, we conduct a case study, evaluate the iTUAV performance, and compare it to benchmarks. Obtained results show that with only 10 anchors in the area, the iTUAV system can serve up to 90% of the users covered by the untethered UAV swapping system. Moreover, results from a small case study prove that the iTUAV allows to balance performance/cost and can be implemented realistically. For instance, when user locations are clustered, with only 2 active iTUAVs and 4 anchors, achieved performance is superior to that of the system with 3 TUAVs, while when considering a single UAV on a 100 minutes event, a system with only 6 anchors outperforms the untethered UAV as it combines location flexibility with increased mission time.