Gemara

(Mishnah): Two Mikva'os join only if the opening between them is at least ki'Shfoferes ha'Nod (the circumference of a hollow reed put into a leather pouch from which one draws out the liquid, i.e. a circle) in which two fingers can rotate around each other.

Chagigah 22a (Rava): If a Mikveh was divided by a basket or Gargusni (a basket used to strain grape juice) and there are not 40 Sa'im on either side, Tevilah is not valid;

Also the ground is porous, yet we do not say that the water is connected (to rivers) to permit Tevilah in less than 40 Sa'im!

Rishonim

Rambam (Hilchos Mikva'os 8:1): Anything connected to a Mikveh is like a Mikveh, and one may immerse in it. If hollows or hoof-prints full of water were connected to a Mikveh by ki'Shfoferes ha'Nod, one may immerse in them.

Source: Mikva'os 6:1 and 5:6.

Rosh (Hilchos Mikva'os (after Maseches Nidah) 15): We need to join Mikva'os when one of them is Kosher and the other is of Mayim She'uvim or is deficient, or both are deficient. The opening between them must be at least ki'Shfoferes ha'Nod, which is (a circle of diameter) two fingers with space so they can rotate around each other inside the hole.

Beis Yosef (YD 201 DH ha'Ba): Toras ha'Bayis says that if one Mikveh is Kosher and the other is of Mayim She'uvim, it suffices if the opening between them is like a hair, since the Pesul of She'uvim is mid'Rabanan.

Poskim

Shulchan Aruch (YD 201:52): If one wants to join a Pasul or deficient Mikveh to a Kosher one, or to join two deficient Mikva'os to make them Kosher, the opening between them must be at least ki'Shfoferes ha'Nod;

Rema: The flow of water must be as wide as the hole.

Shulchan Aruch (ibid.): After they are joined even for a moment, the Pasul one is permanently Kosher, even if the opening was sealed.

Source (Beis Yosef DH u'Mah she'Chosav Rabeinu): The Rosh says so in a Teshuvah (31:2); he brings proofs from three Mikva'os of 20 Sa'im (Mikva'os 6:3) and other places. R. Yerucham was unsure about this.

Taz (62) and Shach (111): Obviously, if it later became deficient we do not say that it is still Kosher.

Shach (112): It is good to be stringent to say that the Pasul Mikveh reverts to being Pasul after the opening is sealed.

Shulchan Aruch (ibid.): If there is a Safek whether or not the opening was ki'Shfoferes ha'Nod, it is Pasul.

Source (Beis Yosef DH Tanan): A Mishnah (Mikva'os 6:7) says that if there is a Safek whether or not the opening was ki'Shfoferes ha'Nod, it is Pasul, because it is mid'Oraisa. I.e. Tevilah is mid'Oraisa.

Shulchan Aruch (ibid.): If there are many small holes they join to ki'Shfoferes ha'Nod if one Mikveh is full and the other is deficient.

Source (Beis Yosef DH Kosav ha'Mordechai): A Mishnah (Mikva'os 6:5) says that one may not immerse in a chest or box in the sea, unless it has a hole the size of ki'Shfoferes ha'Nod. One may immerse inside a bag or basket, because the water mixes (through the pores).

Question: Rava taught that if a Mikveh was divided by a basket or Gargusni we do not say that the pores join to ki'Shfoferes ha'Nod!

Answer (Beis Yosef): That is when there is not a full Mikveh on either side. Rava said that this is like the ground. Even though it is porous, we do not say that the water is connected to permit Tevilah in less than 40 Sa'im! He discusses incomplete Mikva'os. Even though they are separated by porous ground and we see that water transfers, they are not connected. However, if one digs near a full Mikveh or a river and we see that water transfers, they are considered connected.

Chazon Ish (YD 136:3): This is like Avi ha'Ezri. Rashi, the Ri, The Rosh and R. Shimshon say that pores do not join even if one Mikveh is complete. Other Poskim require 40 Sa'im for Tevilas Adam even in a Mayan, yet they could explain our Gemara like Avi ha'Ezri. The Rambam and Ra'avad allow Tevilas Adam in a Mayan of any size, yet they could explain our Gemara like Rashi.

Gra (100): Similarly, if one filled a basket or Gargusni with Kelim and immersed them they are Tehorim. Because there is a full Mikveh outside the basket, it joins through small holes.

Rema: One may dig a Mikveh next to the river and immerse in it, even if it does not have 40 Sa'im. Because the ground is porous and the Mikveh is near the river and we see water coming from the river to the Mikveh, it is considered connected.

Pischei Teshuvah (38): This is from the Mordechai, who holds that a Mayan of any size is Metaher. Most disagree. Unless one is small, there must always be 40 Sa'im where he immerses. It is very rare to see water coming from the river to the Mikveh.

Devar Avraham (1:17:5): Small holes join to ki'Shfoferes ha'Nod only if there is no Hefsek between the Mikva'os that is not Kosher for Tevilah even if we consider them joined. This is why a Mikveh is not considered connected to the river (even according to the Rema, unless one sees water coming).

Shulchan Aruch (ibid.): If both Mikva'os are deficient, the holes do not join to ki'Shfoferes ha'Nod.

Rema: The same applies if a Mikveh was divided by a basket or bag and there are not 40 Sa'im on either side.

Shulchan Aruch (53): If one wants to make a Mikveh of Mayim She'uvim Kosher through Hashakah to a Kosher Mikveh, it suffices to connect them by (the circumference of) a hair, and even if the connection (is not on top and) does not see the air.

Question (Bach): In Sa'if 7, an opening the size of an olive is required!

Answer (Shach 116): Here we are more lenient because there is a complete Mikveh and the Pesul of She'uvim is mid'Rabanan.

Rema: This is only for the Pesul of She'uvim, which is mid'Rabanan. For a Pesul mid'Oraisa, an opening ki'Shfoferes ha'Nod is required.

Taz (63): The Pesul of She'uvim is mid'Rabanan when She'uvim is the minority, like the Rema said above (Sa'if 3).

Rema: Some disagree even regarding the Pesul of She'uvim. It is proper to be stringent.

Shach (117): This opinion holds that a Mikveh that is mostly She'uvim is Pasul mid'Oraisa. However, when She'uvim is the minority all agree that an opening like a hair suffices.