I think Yigor u trust too much statistics and website's evaluations. What's the value of chessok's assesment?
Sure, as a professional mathematician, I'm obliged to trust statistics and computer's evaluations. Nevertheless, I don't neglect your insight since it's your specialty. 
as a mathematician, u should know that statistics can be untrustworthy and will u reinvent the wheel with computer's help? not sure.
Just try to analyze with your mind or at least using some sources, far better than statistics.
As a titled player, i can assure you that i don't know any good player studying/analyzing an opening with statistics.
IM Poucin: Thanks! Well, it's too late for me to improve my chess skills significantly. It's not my goal. At this moment, I'm mainly interested in the classification of openings through pawn structures.
Soloviov should be aware that analysis is of no great value if you have not developed any minor pieces after 10-11 moves or so. Current praxis (mostly from correspondence chess) shows that white isn't doing that great.
All in all, why give white the target of 2. ...Nc6?
Just play 2. ...e6 with the possibility of an improved French or possibly 2. ...g6, since 1. g6 is, after all, one of the main moves against 1. a3. There's no need for ...Nc6 unless it leads to an obvious advantage for black.
What kind of "target"? White gets no development advantage by chasing the knight, and his pawn structure after the chase is far from ideal.
It's never been about the destination (post-pawn structure)....& u know that IM pfren. It's about the journey (the chase & bully).
It actually looks somewhat like the beginnings of a Delayed Wing Gambit or derivative of....
i play this all the time and if i get the chance i play it and i also play it OTB
Why would it be an improve french?
Wing gambit against french is a reliable weapon though, but white can play in another way, for example :
On 2...g6, a way for white to play is :
Really i've never played this a3 idea with white, but it is interesting and be aware about abstract ideas like I play like an improved french, i play a good dragon, etc... Because positions are a bit different (and maybe not to everyone's taste when u play sicilian svechnikov or Paulsen for instance) and moreover, set concrete problems. Maybe it is bad for white, but there is no simple way to handle it with black, very tricky.
2. a3 seems pretty small-minded & passive-aggressive. But who cares, right ?....only 'cuz commitment is actually a parta the risk side of risk vs reward.
1. e4 c5 2. a3 Nc6 looks cool but 3. b4!? is a definitely dubious gambit.
N.B. Sicilian: Mengarini Variation can be also obtained from Anderssen's Opening: 1. a3 c5 2. e4.
I found this gambit from a video here in the spicy gambit series, Since I am not a premium member I could not check my perfomance in this line with chess.com opening explorer, if you could do that , please let me know my perfomance in this gambit. I think I won majority of them but against lower rated players, this makes the Sicilian player discomfort , and the psychological move works ,but as the rating goes higher the efficiency of this gambit and this psychology tends to be lower.
Use openingtree.com
An interesting line which partially accepts the gambit (takes one pawn, but not the other): e4 c5 a3 e6 b4 cxb (accepts) axb Nf6 (declines, instead of Bxb4) e5 Nd5 b5 d6. Which side do you prefer? Can white still carry out a strong attack?
An interesting line which partially accepts the gambit (takes one pawn, but not the other): e4 c5 a3 e6 b4 cxb (accepts) axb Nf6 (declines, instead of Bxb4) e5 Nd5 b5 d6. Which side do you prefer? Can white still carry out a strong attack?
I've never faced that line... everyone goes Bxb4 in that position
Actually, it seems that the best continuation in Mengarini variation with 2...Nc6 is not 3. b4!? but 3. Nf3 or 3. Nc3. So, U just make the transition to the classical Open or Closed Sicilian. But IM poucin says that it makes no sense putting the thick cross on Mengarini variation.
"it seems," What makes u fell 3.Nf3 or 3.Nc3 is better than b4?
What would be the point to play 3.Nf3 or 3.Nc3 when u can play them at move 2 and then play something more useful than a3?
We cannot say that provoking Nc6 is an issue for black...
About the variation given by pfren, here is most of the analysis provided by Soloviov in his "Modern Anti Sicilian a3" :
I think Yigor u trust too much statistics and website's evaluations. What's the value of chessok's assesment?
About Soloviov's analysis, black has some improvments, but this is not so simple.