Assembling epoxy, one of the most common and widely used thermosets, by welding with remote control is extremely difficult and has not been realized so far, as epoxy cannot melt or be dissolved. Here we present a very simple but highly efficient solution by exploring the photothermal effect of carbon nanotubes (CNTs) to manipulate the transesterification reaction in vitrimers. The carbon nanotube dispersed vitrimer epoxy presented here can be welded by light within seconds or minutes. Moreover, various CNT–vitrimer epoxy materials with different chemical compositions and physical properties can be joined together. Furthermore, transmission welding can be used to weld CNT–vitrimers with other kinds of epoxy or thermoplastic polymers, which is not applicable to welding by direct heating and impossible to realize using the currently available photoweldable covalently cross-linked polymer networks. Additionally, these networks can be efficiently healed by light without the involvement of any glue or sealing agents.