This article focuses on quality improvement in the development of DO-178C/ED-12C safety-critical software, optimizing development costs through the implementation of a "continuous certification" integral process. We discuss the major problems associated with traditional, V-cycle software development practices, and highlight the many advantages of adopting a "continuous certification" process based on a more Agile approach. The article proposes a framework for deploying this process, explaining the development of the framework and demonstrating its compliance with the requirements of certification standards. We also propose a tooling based on open-source, off-the-shelf solutions to implement the framework and illustrate its efficiency and effectiveness on an industrial case study.