Due to the great flexibility and innate simplicity of wireless networks, many applications are now realized with wireless connectivity at their core. Countless novel applications are enabled this way and legacy applications are transferred to mobile networks to reap the same benefits. As the networks evolve, applications are becoming ever more demanding, particularly with respect to high reliability and low latency. A common way to achieve high reliability in wireless communications is adding redundant communication channels by means of multi-connectivity. This comes at the cost of additional radio resources that could have been used by other connections. However, multiple links are not always required to achieve the desired reliability. Thus, we propose to combine multi-connectivity with rateless coding as a strategy for efficient resource usage in reliable wireless communications. The proposed schemes consider an erasure channel, and can therefore be implemented on the application layer, making them suitable for use with different physical layer wireless technologies simultaneously. We start out with a single-user analysis and then extend our discussion to multi-user scenarios. Our approach is compared against standardized packet duplication with our analytical framework and by means of simulation. The results with rateless coding show significant gains with respect to the required resources and feedback transmissions.