Transitivity of uncorrelated random variables? Suppose $cov(X,Y)=0\;$ and $\;cov(Y,M)=0$. Does this imply $cov(X,M)=0\;$, if all distinct RV are normal? 

In general, no. Take $X = M$ ;)
It also does not hold if $(X,Y,Z)$ follow a Multivariate Normal $(\mu,\Sigma)$.
Necessary and sufficient conditions for a matrix to be a covariance matrix $(\Sigma)$ are presented here. A matrix is a covariance matrix if and only if it is positive semi-definite.
Hence, take
$$\Sigma =\left( \begin{array}{ccc}
1 & 0 & 0 \\
0 & 1 & 1 \\
0 & 1 & 1 \end{array} \right)$$
and observe that $Cov(X,Y) = Cov(X,Z) = 0$ but $Cov(Y,Z)=1$.
