try using "circulation" instead of movement system.

Not sure where you live, but where I practice, you can't have occupancies in exit stairs. Perhaps look into Fumihiko Maki for a way to approach non life-safety circulation.

How many storys?

Will you have elevators? 

Lot of folks never use the stairs in a residential tower unless there's an emergency.

Well, the issue here is not the the staircase per se, but the way in which the tenants get to their apartments, and whether I could transform this mundane everyday journey to a more appealing stroll. The stairs/elevators would still be doing their main job, I just don't want a generic staircase/elevator which we can find at any residential tower (or any tower for that matter). 

Habitat 67 is an example of how I plan this housing complex to be, so I can't tell how many stories there are. Also, BIG's 8 house is an example of how we can transform the circulation in a residential tower in way that is shapes the building and its dynamics as a whole.

^ have you been to Habitat67?

It's impossible to understand it's "streets" and "neighbourhoods" without walking through them.  Just be careful if you do, their security does not like random people walking around. Don't ask how I know this. Safdie has some great early writings from that time too.

This may be of interest to you.

http://www.architectmagazine.com/technology/thyssenkrupp-announces-horizontal-elevator-prototype_o

Have a vertical garden on one side or three sepperated by some glass and use this to circulate air from the bottom to the top of the building.

I hope you will study the concept of defensible space and the epic failure of design and administration that is the us public housing projects.

If you have HBO check out the mini series Show Me a Hero to grasp the nasty realities of public affordable housing and the politics surrounding it

"Lot of folks never use the stairs in a residential tower unless there's an emergency."

That's because most stairs in a residential tower are specifically designed to be used only in an emergency. Even a residence with some sort of grand experiential circulation will need these boring enclosed egress columns, and most budgets simply don't allow for both.

I second Fumihiko Maki. It's not a residence, but look at his Media Lab Extension at MIT. Beautiful circulation and cross-sectional transparency. Another great MIT project, movement-wise, is Aalto's Baker House.

It is hard for folks to go up stairs more than 4-5 floors. Most folks will want to take a lift up and walk down if it doesn't take too much time, the speed an elevator can move people up and down is significantly less than taking the stairs once you are over 4 floors.

In housing complexes the stairs that are secluded and are places where you can be assaulted (see previous reference on defensible space) and not be seen by people in the building is unsafe and uninviting. Glass walls or strategically placed windows or monumental stairs in an atrium would be safe but stairs can be places where you can be ambushed and thus people will avoid them if they are fully enclosed and secluded, they are often designed like vertical dark alleys with blind corners at every floor.

The thought you share is awesome, your idea is so creative. One should have to think it from initially to implement any such thing at house. After going through all this things I just want to suggest you, search for fold-able pattern staircase. For a  roughly thought  I say, you can make stairs floor by floor which will be open as we pull the trigger and after our use again we can fold it to wall or terrace slab. One more option is you can go with spiral stairs, ts too generic but contain a much less space then any other type of stairs.