Yevamos, Chapter 12, Mishnah 3. This mishnah discusses the three components of the act of chalitzah:
Removing the shoe - taking the shoe off the foot of the yavam.
The spitting - she spits before him.
The recitation - both of them, he and she, recite certain verses from the Torah.
The words of the mishnah - what invalidates and what does not:
"Chaltzah v'rakkah aval lo kar'ah" - she performed the chalitzah and spat before him, but did not recite the passage: "chalitzatah kesheirah" - her chalitzah is valid.
"Kar'ah v'rakkah aval lo chaltzah" - she recited the passages and spat, but did not remove the shoe: "chalitzatah pesulah" - her chalitzah is invalid, since it is missing the most basic component of chalitzah, the removal of the shoe.
"Chaltzah v'kar'ah aval lo rakkah" - here the Tannaim disagree: Rabbi Eliezer says - her chalitzah is invalid. Rabbi Akiva says - her chalitzah is valid, for although the spitting is part of the order of the mitzvah, it does not affect the validity of the chalitzah.
Rabbi Eliezer's approach:
Rabbi Eliezer seeks to ground his position, that the spitting is an indispensable component, in the wording of the verse describing the process of chalitzah in the Torah: "kachah yei'aseh la'ish" - so shall be done to the man. The word "kachah," "so," indicates that the matter must be done in precisely this manner, and from here we learn that anything included in the category of "yei'aseh," of being done, is indispensable to the chalitzah. But what falls into that category? Things that constitute a ma'aseh, an actual deed. Accordingly, the removal of the shoe is a deed and the spitting is a deed, and both are indispensable; the recitation, however, the words she is meant to say, is not considered a physical act, and therefore is not indispensable.
Rabbi Akiva's response:
Rabbi Akiva answers: "Mi sham ra'ayah?" - who says there is any proof from here that the spitting is required? The verse says "kachah yei'aseh la'ish", and its meaning is: anything that is a deed performed on the man, an act that actually touches his person, and that is the removal of his shoe. The spitting, even though it is done before him, does not touch him at all, and since it does not touch him it is not considered a deed performed on the man and is not included in "yei'aseh la'ish"; it is merely something done in front of the man. Therefore, even if she did not spit, the chalitzah is valid.
In summary: In this mishnah we examined the three components of chalitzah - removing the shoe, the spitting and the recitation - and the degree to which each is indispensable: removing the shoe is indispensable according to all opinions, the recitation is not indispensable, and regarding the spitting Rabbi Eliezer and Rabbi Akiva disagree. Both expound the verse "kachah yei'aseh la'ish": Rabbi Eliezer derives from "yei'aseh" that anything which is a deed is indispensable, including the spitting; Rabbi Akiva derives from "la'ish" that only a deed which touches the man himself is indispensable, and therefore the spitting, which is done merely before him, is not indispensable.