We use ab initio and parametrized calculations to investigate the morphology and structural stability at the growing edge of multiwall carbon nanotubes. We find that these open-ended structures are stabilized against dome closure by strong covalent bonds connecting the exposed edges of adjacent walls. Growth at the open edge involves rearrangement of these bonds, which are mediated by carbon atoms bridging the gap and change the tip morphology significantly. Presence of a strong ``lip-lip'' interaction can explain formation of carbon nanotubes under annealing conditions.