This paper presents the design and evaluation of clean-slate transport layer protocols for the MobilityFirst (MF) future Internet architecture based on the concept of named objects. The MF architecture is a specific realization of the emerging class of Information Centric Networks (ICN) that are designed to support new modes of communication based on names of information objects rather than their network addresses or locators. ICN architectures including MF are characterized by the following distinctive features: (a) use of names to identify sources and sinks of information; (b) storage of information at routers within the network in order to support content caching and disconnection; (c) multicasting and anycasting as integral network services; and in the MF case (d) hop-by-hop reliability protocols between routers in the network. These properties have significant implications for transport layer protocol design since the current Internet transports (TCP and UDP) were designed for the end-to-end Internet principle which uses address based routing with minimal functionality (i.e. no storage or reliability mechanisms) within the network. Several use cases including web access, large file transfer, Machine-to-machine and multicast services are considered, leading to an identification of four basic functions needed to constitute a flexible transport protocol for ICN: (i) fragmentation and end-to-end re-sequencing; (ii) lightweight end-to-end error recovery with in-network transport proxies; (iii) optional flow and congestion control mechanisms; and (iv) scalable multicast delivery mechanisms. The design of the MobilityFirst transport protocol (MFTP) framework realizing these features in a modular and flexible manner is presented and discussed. The proposed MFTP protocol is then experimentally evaluated and compared with TCP/IP for a few representative scenarios including mobile data delivery, web content retrieval and disconnected/late binding service. The results show that significant performance gains can be achieved in each case.