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In this paper we introduce confluence relations for motivic Euler sums (alsocalled alternating multiple zeta values) and show that all linear relationsamong motivic Euler sums are exhausted by the confluence relations. Thisdetermines all automorphisms of the de Rham fundamental groupoid of$\mathbb{P}^{1}\setminus\{0,\pm1,\infty\}$ coming from the action of themotivic Galois group of mixed Tate motives over $\mathbb{Z}[1/2]$. Moreover, wealso discuss other applications of the confluence relations such as an explicit$\mathbb{Q}$-linear expansion of a given motivic Euler sum by their basis and$2$-adic integrality of the coefficients in the expansion.

The motivic Galois group of mixed Tate motives over $\mathbb{Z}[1/2]$  and its action on the fundamental group of  $\mathbb{P}^{1}\setminus\{0,\pm1,\infty\}$