1 - The authors could emphasize they can consider different local baths could be.
2 - Scipost is for a general audience, so I would suggest that the authors spend a line or two in explaining what T_1 and T_2 are. Especially since this is discuss early in the paper, but it becomes really clear only in section 3.
3 - I did not find it very clear that the authors were considering both open and periodic boundary conditions. This could be reinforced, for example, in the captions of the figures.
4 - It is also not very clear to me in which parity sector in most of the figures.
5 - I am confused by (9). We have an H^\pm_S on the right-hand side, but on the left-hand side there is no \pm.
6 - One important aspect of topological systems is the presence of the zero-energy modes. This also implies the presence of degeneracies. In this case the authors state that there are no degeneracies due to finite-size effects. However, the master equation used by the authors is a weak coupling equation, and hence it suffers in presence of small energy differences, requiring the use of very small couplings. I would deem important that the authors at least discuss the ideal case, in which there are degeneracies, and the actual case, in which there are very small gaps.
7 - the use of T both for temperature and time scale (although in the second case with a sub-index) is a bit confusing. Maybe use capital \Theta for temperature?
8 - I have recently studied another interesting and very relevant paper by Huang et al. "Dissipative Majorana quantum wires" arXiv:1812.04471
It seems to me that this paper is very relevant. I would suggest the authors not only to cite it, but also to comment on their findings but also to compare them to theirs.
9 - do the authors have a deeper understanding of the change in the occupation of the modes shown in Fig.10? The exact one seems to follow an Airy function profile, but independent of what the shape of the function really is, it would be good to provide some understanding.
10 - I find that the summary could be extended. It is too coincise to have a good overview of the paper. In particular, the sentence "In each of the two subspace..." until "towards the degenerate ground state" is not clear to me.
After this changes have been considered, I recommend the paper for publication.