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@@ -545,6 +545,14 @@ \subsection{Alignments withthe cosmic web}
 angular momentum tends to be perpendicular to the filament direction,
 in the case of sheets it tends to lie perpendicular to the sheet plane.
 
+In the GS we already see an anti-alignment signature with the third eigenvector,
+lower than for RS samples but still significant, this is an expected result,
+even for random pairs with separations of the same order of the scale-lenght of 
+underlying environment, just because individual pair members are more likely to lie 
+following the density distribution. For instance, in a filamentary density distribution, random 
+pairs are more likely to lie along the filament; and in walls, random pairs are more likely
+to lie in the wall.
+
 Can the increase of the alignment strength in the different samples be
 explained as a consequence of different mass dependencies as in the
 results in the previous section? The answer is no. 
@@ -557,8 +565,8 @@ \subsection{Alignments withthe cosmic web}
 samples, the median of $\mu$ decreases as we tighten constraints
 on the pairs, but not as a result of the narrowing mass selection. 
 
-We explored the main differences between the GS and RS samples which can be
-producing this alignment strength feature, and we have that RS samples contraint
+We also explored the main orbit differences between the GS and RS  which could be
+responsible of this alignment strength feature, and we have that RS samples contraint
 the tangential velocity, then pair orbits are more eccentric as we tighten pair
 constraints, and for GS sample there is no tangential velocity constraint at all.
 Therefore, to study any relation between orbit eccentricity and alignment, we 
@@ -567,8 +575,8 @@ \subsection{Alignments withthe cosmic web}
 masses and initial conditions given by current velocity vector and separation.
 We found that eccentricity is not responsible for this alignement feature by
 selecting a subsample of GS having the same eccentricity than 
-2$\sigma$-3$\sigma$ samples, and we found no increase in the alignment of 
-this subsample with GS. 
+2$\sigma$-3$\sigma$ samples where we found no increase in the alignment when
+compared with the full GS. 
 
 
 {\bf Radial Vector}.  Figure \ref{fig:alignment_r} presents the
@@ -662,16 +670,16 @@ \section{Discussion and Conclusions}
 the scope of the work presented here.
 
 These alignments for the LG pairs could be in contradiction with
-findings
+some findings
 \citep{2005ApJ...629..219Z,2008MNRAS.390.1133B,2014MNRAS.443.1274L}
 that report a universal trend where the eigenvector $\hat{e}_{3}$
 (i.e. the filament direction) marks the infall direction for
 substructures. The Milky Way satellites are located at high
 galactic latitudes, almost perpendicular to the vector pointing
-towards the Andromeda Galaxy, which is the direction that we find aligned with
+towards the Andromeda Galaxy, which is the direction that we found aligned with
 $\hat{e}_3$.  
 
-If the alignment we find in this paper holds, this would imply that
+If the alignment we found in this paper holds, this would imply that
 infall in the case of the Milky Way is perpendicular to $\hat{e}_3$,
 in contradiction to the accretion along filaments. If the universal accretion
 along filaments holds, that would imply that that the Andromeda
@@ -689,7 +697,7 @@ \section{Discussion and Conclusions}
 signals \citep{2005A&A...431..517K,2013ApJ...766..120C}, should
 inform us about the structural evolution of the cosmic web.  
 
-Our results also raise the need to observationally constrain
+Our results also raise the need to observationally constraint
 the alignments of LG pairs with their cosmic web environment. To this end
 one could use mass reconstructions from large surveys
 \citep{2009MNRAS.394..398W,2011MNRAS.417.1303M,2014arXiv1407.3451W,2014arXiv1406.1004N}