Type II clathrate hydrates (CHs), or ice clathrates, are inclusion compounds in which a hydrogen-bonded cage-like structure of H2O accommodates molecules of suitable size, known as "guest molecules". CHs have similar local geometrical arrangements of the hydrogen-bonded water network as ice and both are known to collapse to amorphous states on isothermal pressurization at temperatures below about 140 K. Moreover, the collapsed CH states undergo a glass, or glass-like, transition at 140 K on heating at 1 GPa, which is identical to that of collapsed ice, or high density amorphous ice. Here we use thermal conductivity and dielectric measurements to study the transition behavior of two type II CHs with tetrahydrofuran and 1,3 dioxolane, respectively, as guest molecules. After their collapsed states have been heated to well above the glass transition at 1 GPa, we find transitions corresponding to the high to low density amorphous ice transition of ice with only slightly shifted temperature-pressure (T-p) coordinates compared to those of pure water. Thus, collapsed CHs show the same transition behaviors as cold water, which provide the basis for the model that explains the unusual temperature and pressure behaviors of water's properties in terms of two distinct types of liquid water. Collapsed CHs are, however, more stable than collapsed ice and can therefore be studied in a wider T-p interval. The results suggest sluggish homogenizing and phase separation processes, which affect the transition behaviors of collapsed CHs.