Since the first report of very-high density amorphous ice (VHDA) in 2001 [T. Loerting et al., Phys. Chem. Chem. Phys. 3, 5355-5357 (2001)], the status of VHDA as a distinct amorphous ice has been debated. We here study VHDA and its relation to expanded high density amorphous ice (eHDA) on the basis of isobaric heating experiments. VHDA was heated at 0.1 ≤ p ≤ 0.7 GPa, and eHDA was heated at 1.1 ≤ p ≤ 1.6 GPa to achieve interconversion. The behavior upon heating is monitored using in situ volumetry as well as ex situ X-ray diffraction and differential scanning calorimetry. We do not observe a sharp transition for any of the isobaric experiments. Instead, a continuous expansion (VHDA) or densification (eHDA) marks the interconversion. This suggests that a continuum of states exists between VHDA and HDA, at least in the temperature range studied here. This further suggests that VHDA is the most relaxed amorphous ice at high pressures and eHDA is the most relaxed amorphous ice at intermediate pressures. It remains unclear whether or not HDA and VHDA experience a sharp transition upon isothermal compression/decompression at low temperature.