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    The article is essentially well written and I am ready to approve it once some corrections have been introduced.

    As a general remark, I would like to see in the introduction a few words relating the philosophy behind the spike distances with phase synchronization that is nowadays quite popular. In fact, to some extent, the measures discussed in the paper are implicitly based on the identification of pseudo-phases (the fraction of time between two spikes is indeed a sort of phase). I believe that this would help the generic reader to familiarize more easily with the various concepts.

        • Please provide a specific suggestion.

    Now I come to the specific points:

    1) I would start with: "The spike distance is an estimator ..." without repeating spike train distance.

        • Done.

    2) The reference to 'relevant spike time' is not much clear. Maybe it is sufficient to state local from the very beginning.

        • Done.

    3) The quality of the various figures is not optimal; Figure 1 needs specific improvements. First of all larger labels are necessary to make it readable. Since it helps to understand the key concepts, this is important.

        • Larger labels were added.

    Moreover, I suggest removing the explicit "t" dependence in most of the variables (it is redundant and makes more difficult to read the figure).

        • The explicit "t" dependence was removed.

    4) "Averaged bivariate" The name is a bit confusing as one initially expects some time average. If it is not possible to change the name, I would at least start the section referring to ensembles of signals (or multivariate signals) to introduce the need to introduce a measure that works in such contexts.

        • The beginning of the Section was rephrased like this:
       “In the case of multivariate datasets consisting of a larger number of spike trains (N > 2) the averaged bivariate
       SPIKE-distance is the bivariate SPIKE-distance averaged over all pairs of spike trains.”

    5) The first time, the authors refers to Fig.3, I would recommend to state that it refers to the same signals analyzed in Fig. 2.

        • Done. Now it reads:
       “Example plots of the dissimilarity profiles obtained for the bivariate and the multivariate example already used in
       Figure 2 are shown in Figure 3.”

    6) When the author refers to "causal moving average", he should be more precise about its definition and mention the size of the window that has been used and should be used in general.

        • I added one sentence:
       “This introduces a parameter, the size of the moving window, which is set
       depending on the time-scale of interest, e.g., short-term behavior or long-term trends.”

    7) There is a misprint: Figure A, must be Figure Xa, I guess.

        • Corrected.

    8) Another misprint is the missing number of another Figure

        • Corrected.

    9) Finally, internal and external triggered times are poorly described. Anyone willing to apply such concepts would be in trouble. Please explain better.

        • These parts were rewritten and now much more detail is provided regarding both the motivation and the execution of these features.

    The updated version has removed almost all of the problems I pointed out.

    As for the reference to phase synchronization, I suggest to add something like

    The building blocks of this indicator are suitably normalized time intervals which are akin to the pseudo-phases often introduced to quantify phase synchronization in weakly irregular signals.

        • Added

    Moreover, I still think that the starting sentence of the section on Averaged bivariate SPIKE-distance should be slightly rephrased. Here is my proposal

    In the case of multivariate datasets consisting of a larger number of spike trains (N>2) it is convenient to average the bivariate SPIKE-distance over all pairs of trains, to obtain the averaged bivariate SPIKE-distance.

        • Included.

    Finally, I confirm that it would be helpful to improve the readability of Fig. 1.

        • Please view figures in 'Full resolution' (first click on the figure and then press the button below the figure).
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