Cloud application portability and optimal resource allocation are of great importance in the realm of Cloud infrastructure provisioning. c-Eclipse is an open-source Cloud Application Management Framework through which users are able to define the description, deployment and management phases of their Cloud applications in a clean and intuitive graphical manner. It is built on top of the well-established Eclipse platform and it adheres to two highly desirable features of Cloud applications: portability and elasticity. In particular, c-Eclipse implements the open, non-proprietary OASIS TOSCA specification for describing the provision, deployment and re-contextualization of applications across different Cloud infrastructures, thereby ensuring application portability. Furthermore, c-Eclipse enables Cloud users to specify elasticity policies that describe how the deployed virtualized resources must be elastically adapted at runtime to match the needs of a dynamic application-workload. In this paper, we introduce the architecture and implementation of c-Eclipse, and describe its key characteristics via a use-case scenario that involves a user creating a description of a 3-tier Cloud application, enriching it with appropriate elasticity policies, submitting it for deployment to two different Cloud providers and, finally, monitoring its execution.