How can I efficiently ensure the connectivity between two triangulations?

Hi all,

I am trying to merge/stitch two triangulations together and I was wondering what could be the most efficient approach to merge two or more 3D surfaces described by their connectivity matrices F and their vertices matrix V?

I must precise that these two surfaces come from a manually segmented full geometry that have been previously split into smaller parts.

Bonus question now, if these two surfaces are coming from different geometries but I still would like to "stitch" them together, how would you efficiently do that? Like if the previous parts of a splitted geometry have been slightly offset from each other, and I want to connect them as they are now.

Thank you

Rom