It is a bit unclear to me how these adepts work and in which ways they are different from those aspected magicians called shamanists.
Shamanists have onlty the spells, abilitis, penalties & spirits powers for which their totem give bonus or penalties.
Totemic adepts should "spend" points for their powers...but are there any specific power? There is any specific power linked with any specific totem?
MitS page 22 mentioned the fact that these Adepts often take geasa: what the utility of such geasa? Ayone here can explain me how really work a shamanic adept?

Shamanic adepts follow a totem, and as a bonus, they can do the Astral Quest ordeal specifically for initiation (through a "spirit quest" or something similar). They get all of the roleplaying penalties of the totem (berserker rage, pacifism, whatever). When their abilities manifest, they tend to imitate the shamanic mask or emulate the totem (killing hands may take the form of claws, for example). I personally also allow additional dice in combat against specific spirits pertaining to the totem, but that's a house rule. More information can be found in the adept section of SOTA:2064, but that's the gist of it.

well, but in SOTA 2064 therwe is nothing but more metamagic, powers and some background, no real explanations of how these adepts ways really work in terms of rules.
The only exception is "magician way": we know that it must spend some of their points to get how much Magic they want and the rest of points for others powers. For "spirit way" we know one must spend points for Astral perception and things like that...
.....but except for that there is no real division between some Adept ways in terms of rules.
A Warrior and a Athlete could have the same powers....but they have different ways only from a "background " point of view, not from the rules point of view.
Shamanic adepts are, for me, teh most unclear ones.
Shamanic adepts seem to be different due to the mention of totems....but how really it works?
I found no explicit quotation of the application of totem bonus/penalties to shamanic adepts but simply I have the feeling that one has to spend power points for powers which should imitate a totem and then take some geasa to imitate the penalties....
Has anyone a canon answer to this?

Your interpretation pretty much is the canon answer. Take powers you think relate to your totem, take Geasa (if you desire) that might mimic your totem's penalties...and call it a day.

ok, but I think geasa are not compulsory since you have to chose them only if lose Magic points

Unfortunately (or, well, at least considered unfortunate by those who like Geasa), they don't really help you out unless you're purchasing a fairly expensive power. The discounted price gets rounded up to the nearest .25, IIRC. If the cost of the power you're after is less than 1 full power point, you're out of luck.

But if you're going for killing hands D, say, only at night, savese you a good chunk.
Intersting . Wonder how I missed that for so long.
Hahnsoo and his MiTS-fu strikes again.
I'm almost gonna be relieved when 4th ed comes out and I can forget about trying to get everything out of that book!

Which, as I've said before, is totally idiotic.

The whole system of adept geasea is totally idiotic. Adepts lose nothing for taking a geas that they wouldn't lose already by just losing the Magic Point. No wonder people are constantly whinning about how geasea are munchkiny; for adepts they are getting something for (effectively) nothing.

Geasa are not muchkinny. Gaesa are a horrendous karma sink -- involuntary ones at least. Why? Because when you initiate to get rid of them, you do NOT get the metamagic technique you would otherwise get.

In effect, if you take a gaes to offset magic loss, intending to initiate to lose it, you've just paid out a LOT of karma to keep use of the power until you initiate.

For instance, I initiate, take a level of improved reflexes and masking.. and take a deadly wound, so I geas the improved reflexes.. keep it.. and a few runs later initiate again and shed the geas. Fine. 7 magic, 1 metamagic.

Instead, I don't take a geas.. and a few runs later initiate again and take a level of improved reflexes and centering. 7 magic, 2 metamagics.

That's true. Why then, are mages penalized when they break a geas? If the future Karma cost is the main balancing factor for geasea, why the estra hit for mages? I contend that the future Karma cost for removing the geas isn't enough of a balancing factor; there's no reason you ever need to remove the geas, and as you said it's actually a better deal for them to just forget buying off the geas and just buy the power a second time when they initiate.