The information transmission problem in a class of wireless multi-user single-antenna half-duplex relay interference networks is studied. In these networks there are multiple clusters of sources. All the terminals in each source cluster desire to transmit independent messages to a single destination, through multiple layers of intermediate half-duplex relays. We adopt a cluster successive relaying (CSR) scheme, which divides each layer of relays into two alternatively activated clusters, in order to efficiently utilize the half-duplex relays. Using the interference alignment technique, we show that by allowing all sources to non-orthogonally transmit information and all relays to participate in the transmission process, a higher sum degrees of freedom (DoF) can be achieved, compared with directly applying existing transmission design in the considered networks.