In MESH you can union two neighboring triangles by deletion of the common edge.
To unite two triangles:
From the Modification menu choose the Union of two triangles item or click “Union of two triangles” button in the tool-bar.
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“Union of two triangles” button
The following dialog box shall appear:
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Enter IDs of nodes forming the required edge in the Edge field (a couple of node IDs separated by a dash) or select this edge in the 3D viewer.
Click the Apply or Apply and Close button.
“The selected triangles”
“The union of two triangles”
See Also a sample TUI Script of a Uniting two Triangles operation.