Alpha actually solves part of the problem. Is there a way to have a view of the plan almost infinitely. I mean, without the html or background part appearing?
Some background will always be present, either the canvas or html page, nothing can be endlessly transparent.
Your camera has a near and far planes, you can only see models in between those planes depth-wise (and within the frustum side borders).
As seanwasere noticed, you need to set your near plane to be positive; to increase visibility you can increase far plane value but not to infinity and it has its side-effects such as more obvious z-fighting.
You can also move your camera close of course, and decrease near value to keep the model inside the frustum.