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We classify wormholes endowed with redshift effects and finite mass intothree types. Type I wormholes have their radial pressure dying out faster, asone moves away from the throat, than any other component of the stress-energyand thus violate the least the local energy conditions. In type II (resp. III)wormholes the radial and transverse pressures are asymptotically proportionaland die out faster (resp. slower) than the energy density. We introduce a noveland generalizable method for deriving, with no cutoff in the stress-energy orgluing, a class of each of the three wormhole types. We focus on type Iwormholes and construct different asymptotically flat solutions with finite,upper- and lower-bounded, mass $M$. It is observed that the radial pressure isnegative, and the null energy condition is violated, only inside a narrowlayer, adjacent to the throat, of relative spacial extent $\epsilon$. Reducingthe relative size of the layer, without harming the condition oftraversability, yields an inverse square law of $\epsilon$ versus $M$ forsupermassive wormholes. We show that the diameter of the shadow of this type Isupermassive wormhole overlaps with that of the black hole candidate at thecenter of the Milky Way and that the recent derivation, using the up-to-datemillimeter-wavelength very long baseline interferometry made in Astrophys. J.\textbf{795} 134 (2014) [arXiv:1409.4690], remains inconclusive.  We show that redshift-free wormholes, with positive energy density, have oneof their barotropic equations of state in the phantom regime (at least in theregion adjacent to the throat), have their stress energy tensor traceless, andare anisotropic. They are all type III wormholes having their variableequations of state approaching 1 and $-1$ at spatial infinity. We alsointroduce a new approach for deriving new redshift-free wormholes.

Confined-exotic-matter wormholes with no gluing effects -- Imaging supermassive wormholes and black holes