Cloud computing is nowadays a popular technology for hosting IT services. However, deploying and reconfiguring complex applications involving multiple software components, which are distributed on many virtual machines running on single or multi-cloud platforms, is error-prone and time-consuming for human administrators. Existing deployment frameworks are most of the time either dedicated to a unique type of application (e.g. JEE applications) or address a single cloud platform (e.g. Amazon EC2). This paper presents a novel distributed application management framework for multi-cloud platforms. It provides a Domain Specific Language (DSL) which allows to describe applications and their execution environments (cloud platforms) in a hierarchical way in order to provide a fine-grained management. This framework implements an asynchronous and parallel deployment protocol which accelerates and make resilient the deployment process. A prototype has been developed to serve conducting intensive experiments with different type of applications (e.g. OSGi application and ubiquitous big data analytics for IoT) over disparate cloud models (e.g. private, hybrid, and multi-cloud), which validate the genericity of the framework. These experiments also demonstrate its efficiency comparing to existing frameworks such as Cloudify.