Premixed flame propagation in obstructed channels with both extremes open is studied by means of computational simulations of the reacting flow equations with a fully-compressible hydrodynamics, transport properties (heat conduction, diffusion and viscosity) and an Arrhenius chemical kinetics. The aim of this paper is to distinguish and scrutinize various regimes of flame propagation in this configuration depending on the geometrical and thermal-chemical parameters. The parametric study includes various channel widths, blockage ratios, and thermal expansion ratios. It is found that the interplay of these three critical parameters determines a regime of flame propagation. Specifically, either a flame propagates quasi-steady, without acceleration, or it experiences three consecutive distinctive phases (quasi-steady propagation, acceleration and saturation). This study is mainly focused on the flame acceleration regime. The accelerating phase is exponential in nature, which correlates well with the theoretical prediction from the literature. The accelerating trend also qualitatively resembles that from semi-open channels, but acceleration is substantially weaker when both extremes are open. Likewise, the identified regime of quasi-steady propagation fits the regime of flame oscillations, found for the low Reynolds number flames. In addition, the machine learning logistic regression algorithm is employed to characterize and differentiate the parametric domains of accelerating and non-accelerating flames.