thread vein
US /ˈθrɛd veɪn/
UK /ˈθrɛd veɪn/

1.
a small, superficial vein, especially one that is visible through the skin as a fine, red, wavy line, often found on the face or legs
:
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She was concerned about the new thread veins appearing on her nose.
•
Laser treatment can be used to remove unsightly thread veins.