We report on a study of the Nernst effect in graphite extended up to 45 T. The Nernst response sharply peaks when a Landau tube is squeezed inside the thermally fuzzy Fermi surface and presents a temperature-independent fixed point when the tube flattens to a single ring. Beyond the quantum limit, the onset of the field-induced phase transition leads to a drastic drop in the Nernst response signaling the sudden vanishing of Landau tubes. The magnitude of this drop suggests the destruction of multiple Landau tubes possibly as a result of simultaneous nesting of the electron and hole pockets.