The Zener polarons recently found in half-doped manganites are usually seen as mixed valence entities ruled by a double exchange Hamiltonian involving only correlated electrons of the metals. They can however be considered as ferrimagnetic local units if the holes are localized on the bridging oxygen atoms as implicitely suggested by recent mean-field ab initio calculations. In the latter case, the physics is ruled by a Heisenberg Hamiltonian involving magnetic oxygen bridges. This paper shows that the spectra resulting from the resolution of both models are analytically identical. This single resulting model spectrum accurately reproduces the spectrum of Zener polarons in Pr0.6Ca0.4MnO3 manganite studied by means of explicitely correlated ab initio calculations. Since the physics supported by each model are different, the analysis of the exact Hamiltonian ground state wave function should a priori enables one to determine the most appropriate model. It will be shown that neither the spectrum nor the wavefunction analysis bring any decisive arguments to settle the question. Such undecidability would probably be encountered in experimental information. [6,7] show an important O to Mn charge transfer, resulting in a localization of the holes on the bridging oxygens. This charge distribution suggests a dominant purely magnetic local order (Mn 3+ O − Mn 3+ ) in which the Zener polarons would be ferrimagnetic entities involving an antiferromagnetic coupling between the magnetic oxygen and the high spin manganese centers. In the latter case the model Hamiltonian which provides a relevant description of the local electronic order is a Heisenberg Hamiltonian. The holes localization has been a matter of debate in the literature and concerns a large number of materials like doped cuprates [8](where there is at most one unpaired electron per metal resulting in a t-J model), nickelates or manganites (in which there are several open-shells per center leading to a double exchange interaction). Besides, as far as the correlated electrons are only localized on the metallic centers, the comparison of the models has been the subject of intense discussion and controversy which ended up with the demonstration that the two models were strictly different and lead to different spectra [9]. The aim of this paper is to show that when considering a magnetic oxygen in the Heisenberg model the analytical resolution of the two Hamiltonians leads to identical spectra. For this purpose we have derived an analytical solution of the Heisenberg Hamiltonian energies for three magnetic centers.Since the discrimination between the two models is impossible from the spectrum determination, we will then adress this question from wavefunction analysis. Indeed, the projection of the ab initio ground state wavefunction onto both model spaces should a priori determine the choice. However, it will be shown that when the charge of the oxygen is around -1.5, the wavefunction analysis does not infer any decidable argument. In order to illustrate this asserti...