Spectral Sequence involving "Triple Tor" Can someone help me with the first 4 lines of Page 111 of Local Algebra by Serre? 

I would like to know which spectral sequence is being used. 

Initially I thought it is the Grothendieck spectral sequence, but I don't think that is the case, and I don't know what a "Triple Tor" is. Any help would be appreciated. Thank you.
 A: Basically he's computing the homology of the complex $M \otimes^{\mathbb{L}}N \otimes^{\mathbb{L}} k$ (where tensors are taken over $A$). Associativity of the tensor product tells us that
$$
(M\otimes^{\mathbb{L}}N) \otimes^{\mathbb{L}} k = M \otimes^{\mathbb{L}}(N \otimes^{\mathbb{L}} k)
$$
And so we get two different spectral sequences...
$$
\operatorname{Tor}_p(\operatorname{Tor}_q(M, N), k) \Rightarrow \operatorname{Tor}_{p+q}(M, N, k)
$$
$$
\operatorname{Tor}_p(M, \operatorname{Tor}_q(N,k)) \Rightarrow \operatorname{Tor}_{p+q}(M, N, k)
$$
which you can think of in many different ways. One comes from the spectral sequence associated to a double complex. That is, in general if we have complexes $A_*$ and $B_*$ and we want to compute $H_*(A_* \otimes^{\mathbb{L}} B_*)$ (this is sometimes called "hypertor" but that makes it sound scarier than it is...) then we can choose Cartan-Eilenberg resolutions $P \rightarrow A$ and $Q \rightarrow B$, and consider the spectral sequence of the double complex $P \otimes Q$. This gives:
$$
H_*(H_*(A) \otimes^{\mathbb{L}} H_*(B)) \Rightarrow H_*(A \otimes^{\mathbb{L}} B)
$$
which specializes to the aforementioned spectral sequences in your example.
