This work deals with unsupervised change detection in bi-date Synthetic Aperture Radar (SAR) images. Whatever the indicator of change used to compute the criterion image, e.g. log-ratio or Kullback-Leibler divergence between images, we have observed poor quality change maps for some events when using the Hidden Markov Chain (HMC) model we focus on in this work. The main reason comes from the stationary assumption involved in this model --and in most Markovian models such as Hidden Markov Random Fields--, which can not be justified in most observed scenes: changed areas are not necessarily stationary in the image. Besides the non-stationary Markov models proposed in the literature, the aim of this paper is to describe a pragmatic solution to tackle change detection stationarity by evaluating and comparing a 1D and a 2D window approaches. By moving the window through the criterion image, the process is able to produce a change map which can better exhibit non-stationary changes than the classical HMC applied directly on the whole criterion image. Special care is devoted to the estimation of the number of classes in each window, which can vary from one (no change) to three (positive change, negative change and no change) by using the corrected Akaike Information Criterion suited to small samples. The quality assessment of the proposed approaches is achieved with a pair of RADARSAT images bracketing the Mount Nyiragongo volcano eruption event in January 2002. The available ground truth confirms the effectiveness of the proposed approach compared to a classical HMC-based strategy.