On the one hand the present globalisation process has only been made possible through a reduction of time-distances allowed by high speeds, and particularly through the development of the air mode. On the other hand the metropolisation process seen as the urban counterpart of globalisation is deeply associated with the development of air platforms. Understanding distances between places is a fundamental task for the geographer, while the representation of distances constitutes one of the major functions of cartography. Among the types of maps invented to represent time-space anamorphosis have been supplemented in the 1990's with time-space relief cartography. This paper proposes a representation of the time-space relief of the USA considering terrestrial and air modes. This last point constitutes a key innovation among this type of cartography, giving the possibility to build a representation of global time-space. The metaphors associated with the images proposed are then discussed evocating the shrinking, the crumpling and finally the shrivelling of time-space. The shrivelling metaphor renders account of the complicate contraction/dilatation movement that thigh speeds provokes on space and allows for a rich interpretation of the time-space relief map of the USA in the perspective of the processes of globalisation and metropolisation.