といえば

と言いう packages a name or idea as content, open-ended after it. と言いえば instead launches a fresh topic, by whatever the speaker connects to N.

といえば takes its cue from what was just said, by association (京都きょうとといえば、紅葉こうようですね). ところで drops the old topic entirely, with no link needed at all.

Ordinary ば asks a real "if" (言いえば, "if you say"). と言いえば has frozen into a fixed topic starter ("speaking of…"), asking nothing.

と言いえば picks up a noun just mentioned and drifts from it (日本にほんと言いえば). から言いえば makes that noun the measure for a verdict (日本にほんから言いえば).

というと after a topic just mentioned starts talking about it (京都きょうとというと紅葉こうようだ). Inside なぜかというと, that same というと just closes a question, with no topic involved.

といえば needs a named topic right before it, and jumps off from that word (日本にほん料理りょうりといえば寿司すしだね). そういえば instead stands alone, with no word needed in front of it (そういえば、あの件けんどうなった？).

と言いえば free-associates off a topic just mentioned, launching a new thought (日本にほんと言いえば、寿司すしだね). と言いっても walks back a claim just made instead, introducing nothing new (人気にんきと言いっても、一部いちぶだけ).

といえば opens a new topic by association (京都きょうとといえば). というか takes back the word just said instead (疲つかれたというか).

といえば picks up the word just said as a new topic (京都きょうとといえば、紅葉こうようだ). とはいえ instead concedes what was said and turns against it.