Just play lightly and everything is going to be OK!: Legato third

Practice playing third intervals smoothly

Phrases with a series of thirds are very common, but to play them lightly and legato requires a special technique. Here’s the idea. After playing the first third (say right hand C and E, played together with 1 and 3 fingerings), then hold E while you raise the other finger from C; then play D and F together. Watch the video to see how it done.

Just play lightly and everything is going to be OK! Series

https://www.youtube.com/playlist?list=PLudx7iyi4eXQKJJ44RnTgRdERTAXTG_KX

You can practice more with this technique:

Hanon No.15 and Czerny No. 9 and 10 Play Along

Hanon

complete score --- https://imslp.org/wiki/The_Virtuoso_Pianist_(Hanon,_Charles-Louis)

This is good website, too --- https://www.hanon-online.com

Czerny

complete score --- https://pianoexercises.org/exercises/czerny/)

specially I uses "125 Exercises in Passage Playing"

https://pianoexercises.org/exercises/czerny/

Schubert 18 Viennese Ladies' Ländler D.734, Op.67

https://imslp.org/wiki/Wiener_Damen-Ländler_und_Ecossaisen%2C_D.734_(Schubert%2C_Franz)