In this talk, we study the effect of non-unitarity with active-neutrino-sterile-neutrino mixing in the expected high-energy astrophysical neutrino flavor content. Non-unitarity in the measurement of the three-active neutrinos can be due to the existence of sterile neutrino states. We introduce the concept of the four-flavor tetrahedron in order to visualize the lack of unitarity in the astrophysical neutrino three-flavor triangle, and we discuss the further modifications in the presence of source astrophysical sterile neutrinos. Using current global fit constraints including the non-unitarity case, we also illustrate the allowed astrophysical neutrino flavor ratios. Measurements of the high-energy astrophysical neutrino flavor content could explore sterile neutrinos independently of the sterile neutrino mass scale. These are topics of investigation for current and future neutrino telescopes.