To define a traversable wormhole, there should be some conditions on the metric components, such as:
I) No event horizon,
II) Minimum value for the shape function (considering a spherical symmetric solution, we should have $b(r_t)=r_t$ ),
III) The flare--out condition ($b'(r_t)<1)$ ans ...
If this condition satisfies besides the null energy condition, we have a traversable wormhole solution with nonexotic matter.
My question is that, could we describe the spacetime through the throat with the wormhole metric or it is another patch? It seems that on the above conditions, it is not possible to use the mentioned wormhole solution in the throat. But, then, why in the literature this metric is used for throat passage description?