The ability to reshape nanopores and observe their shrinkage under an electron microscope is a powerful and novel technique. It increases the sensitivity of the resistive pulse sensing and enables to detect very short and small molecules. However, this has not yet been shown for glass nanocapillaries. In contrast to their solid-state nanopore counterparts, nanocapillaries are cheap, easily fabricated and in the production do not necessitate clean room facilities. We show for the first time that quartz nanocapillaries can be shrunken under a scanning electron microscope beam. Since the shrinking is caused by the thermal heating of the electrons, increasing the beam current increases the shrink rate. Higher acceleration voltage on the contrary increases the electron penetration depth and reduces the electron density causing slower shrinkage. This allows us to fine control the shrink rate and to stop the shrinking process at any desired diameter. We show that a shrunken nanocapillary detects DNA translocation with six times higher signal amplitudes than an unmodified nanocapillary. This will open a new path to detect small and short molecules such as proteins or RNA with nanocapillaries.